# Math word problem

• Nov 16th 2013, 03:43 PM
ipinocchio
Math word problem
Hey anyone viewing this, I need help with a word problems they have to be my worst subject considering I ask to much questions on them but I was reading ASVAB AFQT for dummies and stumbled upon a question that got me wondering 'how'd he get that'. Here's the question.

"Jeremy has 12 more nickels than quarters. How many coins does he have if the total value ofhis coins is $2.70" Let q = quarters. Because Jeremy has 12 more nickels than quarters, this could be represented as q + 12. Jeremy has$2.70 worth of coins, which is equal to 270˘. A quarter is 25˘,
and a nickel is 5˘. Jeremy’s total coins together must equal 270˘. Therefore:
(25˘ × number of quarters) + (5˘ × number of nickels) = 270˘
Or, writing it another way:
25q + 5(q + 12) = 270

I understand some of this but not all of it. Now the part that got me wondering is the formula.
25q+5(q+12)=270. How did he get the 5(q+12). How did he even know how to set the formula like that?
What goes where?

Thanks a bunch, please no rude comments if he stated it in the explanation.
• Nov 16th 2013, 03:54 PM
sakonpure6
Re: Math word problem
Quote:

How did he get the 5(q+12). How did he even know how to set the formula like that?
What goes where?
Well we know he has 12 more coins nickles than his quarters, so (12+q) represents that he has 12 more than his quarters. Now what the "5" represents is the value of the nickle (in cents).

25q : 25 represents the value of a quarter in cents, and q is the amount he has.

So, the question tells us that when he has both amount of quarters and nickles he has 270 cents
So,
25q + 5(q+12) = 270
25q + 5q + 60 =270
30q = 210
q= 210/30
q= 7

There fore he has 7 quarters and (q+12) -> (7+12) = 19 nickles.

To check, is this true : 25(7) + 5(19) = 270?

Yes, then our solution is right.
• Nov 16th 2013, 04:00 PM
SlipEternal
Re: Math word problem
The letter $\displaystyle q$ represents an unknown number of quarters. A quarter is worth 25 cents. So, if you have 2 quarters, you have $\displaystyle 25 \times 2$ cents worth of quarters. If you have 3 quarters, you have $\displaystyle 25\times 3$ cents worth of quarters. Then, if you have $\displaystyle q$ quarters, you have $\displaystyle 25\times q = 25q$ cents worth of quarters.

Suppose Jeremy has 0 quarters. Since he has 12 more nickels than quarters, he would have $\displaystyle 0+12 = 12$ nickels. If Jeremy had $\displaystyle 1$ quarters, then twelve more than that would be $\displaystyle 1+12 = 13$ nickels. If Jeremy had $\displaystyle 87$ quarters, then twelve more than that would be $\displaystyle 87+12 = 99$ nickels. So, since Jeremy has $\displaystyle q$ quarters, he has $\displaystyle q+12$ nickels. Since each nickel is worth 5 cents, if he had 12 nickels, he would have $\displaystyle 5 \times 12$ cents worth of nickels. If he had 13 nickels, he would have $\displaystyle 5 \times 13$ cents worth of nickels. If he had 99 nickels, he would have $\displaystyle 5\times 99$ cents worth of nickels. But, we know he has $\displaystyle q+12$ nickels. So, he has $\displaystyle 5\times (q+12) = 5(q+12)$ cents worth of nickels.

So, he has $\displaystyle 25q$ cents worth of quarters and $\displaystyle 5(q+12)$ cents worth of nickels. If he adds that up, that is how much all of his coins together are worth. For example, if he had 4 quarters and $\displaystyle 4+12=16$ nickels, he would have a total of $\displaystyle 25\times 4 = 100$ cents worth of quarters and $\displaystyle 5\times 16 = 80$ cents worth of nickels. Add that together, and he has a total of $\displaystyle 100 + 80 = 180$ cents worth of coins.

So, adding together the value of his quarters plus the value of his nickels, we conclude Jeremy has $\displaystyle 25q+5(q+12)$ cents worth of coins. While we are not sure what $\displaystyle q$ is, we know it cannot change. As we work out the problem, Jeremy will not gain additional quarters or nickels. He will not drop them. So, even though we don't know what the value of $\displaystyle q$ is, we know it will remain the same while we figure out the problem. The same is true for this expression: $\displaystyle 25q+5(q+12)$. It has a value, and that value has a meaning. That expression is the value of all of the nickels and quarters that Jeremy has. We know that value. We are told Jeremy has 270 cents worth of quarters and nickels. So, $\displaystyle 25q + 5(q+12) = 270$. They are the same value. If you add up the value of his quarters and the value of his nickels, it will give you the total value of all of the quarters and nickels that he has.
• Nov 16th 2013, 04:34 PM
ipinocchio
Re: Math word problem
Quote:

Originally Posted by sakonpure6
Now what the "5" represents is the value of the nickle (in cents).

Oh so since a nickle = 5 cents that's the base right?
• Nov 16th 2013, 04:35 PM
ipinocchio
Re: Math word problem
Thanks guys!