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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