4Th Grade Math Word Problem

It's algebra. x= Cindy's age, 3x = Robert's age. x+3x=28. Solve for x, x=7. So Cindy is 7 and Robert is 21. So C is the correct answer. "Cindy's age is 3 times less than Robert's" is just another way of saying "Robert's age is 3 times MORE than Cindy's". And it'll only get harder from here on out - yay for us moms!

The Bella problem can't be 15 and 3...the equation for that one is: 4x - x = 12, right? Bella's brothers age (4x) minus Bella's age (x) is 12 (years difference), right? So then solving for x again, 3x = 12, x = 4. So Bella is 4 and her brother is 16. 15 and 3 don't even work in the equation of 4x - x = 12. The only way it would work if Bella's brother was *5* times older than her. Maybe it was a typo and the "4" should have been a "5", because as written, there's no possibly way it's 3 and 15. Strange...

Very awkward wording! If C is the answer, then the question should say that Cindy is 1/3 of Robert's age. Less than indicates subtraction, not division.

#2: Bella=x; brother=y
y=x+12 and y=4x+x (because it's 4 times MORE, not just 4 times Bella's age)
x+12=4x+x (since they both equal y. Solve for x)
12=4x
3=x

y=x+12
y=3+12
y=15

Bella is 3 and her brother is 15

Wow! If this is so confusing for adults, I can't imagine being in 4th grade!

ETA: I think I understand Busymom's and SH's answers! I don't necessarily agree, but oddly enough I see the logic. I *think* they mean the sentence should have stated: "Cindy's age is 3 times less than their combined age, than Robert's."

This would give us: x=28-3x
4x=28
x=7

y=28-x
y=28-7
y=21

Yes? No? I don't know anymore!

The answer is C. It is a poorly-worded question, though. "Three times less than" should have been one-third. "Less than" usually implies subtraction. Mean question-maker-upper. :-[

HERE'S THE ANSWER:

"Three times" is multiplication. So I now know my answer is going to involve two numbers, and one of them can be multiplied by Three to equal the other one. OR one can be divided by Three to equal the other (as multiplication is merely the opposite of division - therefore related)
7x3=21
or
21divided by 3=7

After you do the multiplication - "Less than" is expressing that one sibling is younger. Therefore we further know that it is Cindy who is seven, and Robert who is 21.

ORIGINAL ANSWER

Oh MY Gosh.

Please don't listen to S.H. Sorry, no offense, but that is not where you put a comma.

A comma is used to show a pause in thought, like that. Or it is used to separate a list of a, b and c. Although some parts of the country do use a, b, and c.

It's 3 times less than. It means, "divided by 3" in math word problem lingo.

I apologize if this was already explained - but please - look it up. There is no such thing as a comma in the phrase "less, than"

ETA: If the teacher says the bella problem is 15 and 3, ask her to send home the math because I am almost sure it is 16 and 4. Here's why:

bella is x, her brother is four times more =4x. The difference (meaning substraction) is twelve, so the equation is 4x-x=12.
So 3x=12, divide by 3.
x=4 Bella is 4 so her brother is 4(4) which equals 16 and 16-4 is twelve.

If cindy is 3 times less, it stands to reason that robert is 3 times more, so:

x (cindy) + 3x (Robert) =28
4x=28
x(cindy)=7
3(7)(Robert)=21

You could also solve for x the long way (the way it's written by 'less than'):

Cindy would be Robert (x) divided by 3, so you would have:

(x/3)(cindy) +x (robert) = 28
Times everything by 3 to get rid of the denominator: x +3x= 84
4x=84
x=21 (robert
So Cindy would be x (21) divided by 3 which = 7.

I think the wording of this word problem is confusing. Where the question has "Cindy's age is 3 times less than Robert's." I would rephrase as "Robert's is 3 times the age of Cindy."

So C. is the correct answer because 7+21=28 and 7*3=21

Bella's brother's age is 15, so Bella is 3 because 3 + 3*4 (her age plus her age times 4) equals 3+12=15. For that one, I would most likely have worked from the given answers to see which one fit the problem's stated facts.

I would encourage you to talk to your child's math teacher. There is definitely two meanings confusingly used with "times less than" and "times more than". Ask the teacher if this wording is as on a standardized test or if he/she would explain and/or change that wording.

Now, I have a 4th grader and I would be quite stuck if I had to teach him how to interpret this word usage!

I don't think I can answer your question about "what grade". I do know that with my 7th grader and 12th grader I did reach a point where I had to say "I don't know the answer. Let's look for it together." Sometimes I said this even though I know the answer and to give them the exercise of looking up a solution or source with the answer.

Good luck!

The wording is not right in my opinion. I don't see how any number can be "three times less" than another at fourth grade math level.
The anwer is obvious to me but the wording would cause me to question my own good sense and I can't imagine expecting a fourth grader to get it.
I'll bet this is one of those practice tests to get the kids ready for the standardized tests. I really cannot beleive some of the questions they ask. They lack common sense, do not encourage critical thinking and are just plain stupid in many cases.

I've taught 3rd and 5th grades in Texas and have never seen any question so oddly phrased. When you gave the choices I thought "Oh well 7 x 3 is 21..... so that works! 3 x 3 is 9 so that works too, but those don't add to equal 28.

The next problem --- I would have thought the answer was 16 and 4 cause 4x4 is 16..... "4 times more" ???? Maybe I'm missing something too?

I know STAR is the new state exam, but if you want to see what an old 4th grade TAKS test looks like, click here and you can see old tests and answer keys for 4th grade all subjects http://www.tea.state.tx.us/student.assessment/taks/releas...

ADDED:
I just read some other answers below. Glad I wasn't the only one that thought your second problem was 16 and 4, NOT 15 and 3. The teacher made a mistake on that one. Plus, I agree that there should be NO comma there. In the 5 years I taught here in Texas never never have I seen a comma there. We teach the children "less than" being a phrase where you are often comparing something.

C=Cindy
R=Robert

Cindy's age and her older cousin Robert's age together equal 28.
C+R=28

Cindy's age is 3 times less than Robert's.
R=3C
Which basically means that Robert is older and he is 3 times older than Cindy.

So you plug in the second equation into the first.
C+3C=28

Solve for C
4C=28
C=7

So Cindy is 7 years old. And going back to second equation you know that Robert is 3 times older than Cindy. So 3 times 7 is 21. So Robert is 21 years old.

definatley c .. i think itsjust the way its worded thats a little confusing .. they should said robert is 3x as old as cindy.. for some reason that doesnt confuse me as much.. btu its defiantley c.. its the only answer that equals 28 and the lower number x3 = the higher number

yes c is right. 7 goes in to 21 3 times and 21 plus 7 is 28. the wording is a little tricky but thats how they make them...

Math is why I never finished college... I can never figure out the wording, but I do see how c is the correct one, it's the only one that fits the requirements for the question.

7x3= 21
7+21= 28

Anyways... this is way too much for 4th grade, ha!

My GD is in 4th grade and I have trouble helping her sometimes. Fortunately, I have two nieces who have just graduated college so they come over and help when needed.

To the question: "Are you smarter than a 4th grader?" The answer is a resounding "NO!"

C is the correct answer because 7 + 21 = 28; and 7 is three times less than 21 (7x3 = 21).

By the way, we are getting algebra and geometry in 4th grade! So far I've been able to keep up with the algebra ONLY because they are not solving for the letter yet. As soon as we have to solve for "A" I'll be done. As for the geometry, I'm done. We use the internet alot for help. You can google anything!

I'm glad to know that I'm not alone here. They only bring home worksheets - no book with an explanation that I can read so unless I can find something on the internet that I can understand, I'm done!

OK, for the first problem,
the problem is worded poorly so it is confusing, but think I can explain it ...

"Cindy's age and her older cousin Robert's age together equal 28."

Let Cindy's age=C and Robert's age=R, and translate from English to Math.
C + R = 28
You probably got this part.

Cindy's age is 3 times less than Robert's.

This is a confusing statement. They probably should have said, "Robert is three times older than Cindy," or "Cindy is one third as old as Robert." If we translate from English to Math, we get:
R = 3 * C [or (1/3) * R = C, the first equation will be easier to use]
(Isn't Math language so much more concise and precise?! The word "less" in the original English statement makes you think subtraction when really they were just conveying that Cindy is younger than Robert by a factor of 3 and not the other way around.)

Now you have two equations:
C + R = 28
R = 3 * C.

Since you know what R is in terms of C (One R equals three C's.) Substitute for R in the first equation.

C + (3 * C) = 28
4 * C = 28
C = 7

Now, if C= 7, and R = 3 * C, R must equal 21. The answer is 7 and 21.

For the second problem, ...

"Bella's brother's age is 4 times more than hers."

Let's let B=Bella's age and Br=Brother's age.

4 * B = Br

[You can check your English-Math translation by substituting real numbers to see if they make sense when translated back to English. For instance, if you let B = 1, then by the Math equation above, Br = 4. If you keep these numbers in mind, and you read the English phrase, it makes sense because Bella's brothers age (4) is 4 times more and Bella's age (1.) If you made a mistake and used B = 4 * Br, you should catch your mistake when you try to substitute the numbers.]

"they're 12 years apart" means that the difference in their ages is 12 years.
From the first statement, we can guess that Bella's brother is the older of the two, so we put him (Br) first in the subtraction equation so that we end up with a positive number
Br - B = 12

Now we have two equations:
4 * B = Br
Br - B = 12

You can substitute 4 different ways in these two problems, but many times you can choose a substitution that is easier (avoids fractions or multiplying alot of numbers.) The simplest way is to substitute for Br from the first equation into the second equation

(4 * B) - B = 12
3 * B = 12
B = 4 and Br = 16.

I believe that 15 and 3 are INCORRECT. Here's why:

While 15 and 3 are 12 years apart, if you substitute 15 and 3 back into the first statement, , "Bella's brother's age is 4 times more than hers" you get 3*4=15, which is not a true statement.

Hope that this helps.

For your original question, my son is in seventh grade, and I occasionally have to help him with very similar math, too. Often, it is on occasions just like this where the problems are poorly worded and sometimes even incorrect. (Who writes this stuff?) so I don't blame him at all for being confused. :)

I think it just means she is 3x younger and "less than" should have not been used.

I am cussing like crazy over here because I just worked both problems out on here step by step with explanations and lost it before I could post. I am so friggin' hot about that! I don't have the energy to explanation it again, but here is how it works out:

Bella's age is B. Her brother's age is b. If her brother's age is 4 times more than hers, then he is her age plus 4 times her age. (They didn't say he is 4 times her age; they said 4 times MORE, which means "in addition to". In addition to her age, add 4 times her age.) b=B+4B. b=5B. And because they are 12 years apart, b-12=B. Soooo...

5B-12=B
4B=12
B=3; b=15

The same logic doesn't seem to be followed with the first problem. (One of them might actually be wrong. Since the wording is consistent--3 times less than, 4 times more than--the process to solution should be, too.) The way that you would get the answer that they say is right is to think that Cindy's age is 1/3 that of her cousin's, which looks like this: C=(1/3)R. If you were to work it out to be consistent with the way the other problem was worked (and worded), it would look like this: C=R-(1/3)R. Example: If beans are 33% more expensive this year (y) than last year (x), then that means that the beans cost 100% of last year's price plus 33% of last year's price, which looks like y=x+(.33)x. If beans cost 33% less (same as 3 times less) this year, then y=x-(.33)x. Cindy's age is 33% less than Robert's age. The solution they have puts Cindy's age at 33% of Robert's age. 33% less than and 33% of aren't the same thing.

(Sometimes they are wrong, so you have to make them show their work, too. I would never just choose one of the multiple choice answers in a case like this and plug it in. I remember when NASA came to our school and put some stuff up on the board. They went through their whole presentation of this particular case, and I raised my hand and told them that I was still trying to figure out how they got one thing in one of the first steps when I had gotten something different. Guess what--they were wrong, and I was right. I'm not saying that I'm right here...just that you have to be able to apply what you've learned to make it make sense to you. You have to feel secure in the process. If it doesn't make sense to you, then you can't be afraid to question it and have the "authorities" show you where the kinks are in your logic. Please update us because I'd really like to know how this turns out.)

I solved it backwards from Kristen C.

Instead of solving for Cindy's age, I solved for Roberts:

R + R/3(this would be Cindy's age) = 28

3R + R = 28x3

4R = 84

R/4 = 84/4

Therefore, Robert's age is 21

Happy mathing!

When my first hit 4th grade he came home with fractions. I looked at his sheet and for a moment I couldn't add or subtract them. lol
After Algebra I have to go to the internet and look things up. I found AP Calculus BC beyond my mommy brain and sent my daughter back to the teacher.

I happen to agree with Kari on this one. Sometimes these story problems are more confusing than they need to be.

These are the type of math questions on the state mandated tests.. They are not math problems with numerals as much as word problems.

Now you realize if a child has trouble reading.. how they have so much trouble passing these tests..

This is also why I could never home school.. I could never convey to our child these types of problems.. Thank goodness for the excellent teachers.

That is the only answer in the multiple choice..where 3x7=21 and 7+21=28.

21 is one times less, 14 is two times less, 7 is three times less "C" is the correct answer

21 is one time less then 28, you know that he number dividing by is 7

to some answer A might seem correct but 6 would be one time less and 3 would be two times less, but to an adult it was obviously taken out because they dont' equal to 28.

It says 3 times less than because you are not supposed to multiply, you are supposed to divide. If you wanted it to say "equal to" you would have to rearrange the question to say something like this: "Robert's age is equal to 3 times as much as Cindy's". Since it is describing Cindy's and she is younger, you have to look at the bigger number in the choices and divide by three. Then you have to make sure they equal 28 together. 21/3 is 7, and 7 + 21 =28. As for the next problem, the answer could very well be 16 and 4 also. When you do the math for it the answer is the same. Is that one multiple choice too? Because both answers would work.

It's C. I'm right there with you with the confusing math homework. Our son's in third grade and I had to write a note on one section of his work tonight that I couldn't figure it out to help him. I can only imagine what nightmare math homework is ahead in the coming years.

3 x 7 = 21 so when she says three times less than twenty one it seems some what logical to find that answer. Idk about the second answer ???

**Adding This:
Hey Dad On Purpose, no offense taken.
But for me, I naturally pause at that point in the sentence.
I asked someone else as well.
Anyway, no biggie.
http://grammar.ccc.commnet.edu/grammar/commas.htm
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The wording should have been "Cindy's age is 3 times less, than Robert's."
Then, the answer "C" is correct.

The way it is written "Cindy's age is 3 times less than Robert's"... makes it a whole other type of math problem.

There should have been a comma, after the word "less."

It does say that TOGETHER they are equal to 28.. if together was omitted , then yes, this would be very confusing even further..
the answer is 7..

I see your confusion with the wording. The wording is not in,a way for mine, and obviously your, brain to process it but my math teach once told me, dont make the problem harder than it just keep it simple and math. Yhat helps me a lot.

Renee (and the others) are spot on. And the correct answer to the second one is definitely 16 and 4, not 15 and 3.

That said, these problems are really (really!) poorly written.

The easiest way (for me) to do this problem, is to divide by 4. That way, you give her 1 part, and him the 3 parts. He is 3 parts older then her, and she is left with the fourth part. Does that make any sense?

ETA:
I would do the next question the same. They are 12 years apart, so I'd put 12 into 4 parts, then add that by 12.