Question

A jar contains only quarters and dimes. The jar contains a total of 92 coins. The value of all the coins is 14$. How many quarters and dimes are in the jar?

Answer 1

read the explanation ya bean bag

Explanation:

we can set up some equations

lets say that q=one quarter and d=one dime

there are 92 coins so q+d=92

for each quarter, there are 25 cents added towards the 14 dollars

for each dime, there are 10 cents added towards the 14 dollars

14 dollars is equal to 1400 cents

using all this information, we can write the following equation:

25q+10d=1400

we can simplify this to 5q+2d=280

remember that q+d=92, so let's take out the extra dimes: 3q+2(q+d)=280 or 3q+2*92=280 or 3q+184=280 or 3q=96 or q=32

there are 32 quarters, so we can subtract 32 from 92 to figure out how many dimes we have

92-32=60 dimes