SOLUTION: An old jar of dimes and quarters contains 200 coins total, and the value of all the coins is $42.50. How many quarters are in the jar? A. 50 B. 130 C. 127 D. 150

Question 1127278: An old jar of dimes and quarters contains 200 coins total, and the value of all the coins is $42.50. How many quarters are in the jar?
A. 50 B. 130 C. 127 D. 150
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
A QUICK FIFTH-GRADER ANSWER:
Using only quarters, you need coins to make .
Using only quarters and dimes, you need an even number of quarters to make .
(Using an odd number of quarters you would make amounts ending in 5)
If you start with quarters,
and swap quarters for dimes,
You would still have ,
but the number of coins would increase by to .
How many such swaps would it take to have a total of coins?
coins is more coins than .
So starting from quarters, you would need
such swaps.
Then you would be using less quarters,
for a total of quarters.
If you can do that quickly, in your head,
you are on your way to a good SAT score,
and maybe a job as a casino dealer.
If you need pencil and paper, you could still do well on the SAT.

ONE SHOW-YOUR-WORK ANSWER FOR ALGEBRA CLASS:
With one variable:

.
The total money amount, in cents, is

You simplify and solve for , maybe like this:

.

ANOTHER SHOW-YOUR-WORK ANSWER FOR ALGEBRA CLASS:
With two variables:

.
The total number of coins is
The total money amount is

(or maybe, in cents, ).
With those two equations we have a system of linear equations to solve by the method of your choice.
Maybe, from ,
you solve for to get .
Then, you substitute for in , get

.
At that point you could also find , the number of dimes,
but nobody asked for that.
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