Question

I have $11.60 in dimes and quarters. I have 32 more dimes than quarters. How many dimes and how many quarters do I have?

Answer 1

D=dimes
Q=quarters

D=32+Q
Q=?
D+Q=$11.6
D=(32*10)+Q=
$3.2+Q
$11.6-$3.2=$8.4
Each quarter must include 1 dime from now on because there’s 32 MORE dimes than quarters. $8.4/$0.35=24. (Divide 8.4 dollars by 1quarter+1dime, which is 35 cents.)

35 cents goes into $8.4 dollars 24 times. This means there’s 24 quarters and 24 more dimes. Returning to our original equations,
D=32+24
D=56
Q=24

This follows the rule of having 32 more dimes than quarters and the two add up to the correct amount, $11.60

There’s 56 dimes and 24 quarters