How many quarters and dimes?

Question

The total value of a collection of quarters and dimes is $3.90. The number of dimes is 27 less than 3 times the number of quarters 

 

Answer 1

The total value of a collection of quarters and dimes is $3.90. The number of dimes is 27 less than 3 times the number of quarters 

 

let d be number of dimes

let q be number of quarters

 

then d=3q-27...Eq 1

 

Now each dime is 10 cents = $0.1

each quarter is 25 cents = $0.25

 

Then 0.1d+0.25q=3.90 is ...Eq 2

Solve for d and q

 

d=3q-27

0.1d+0.25q=3.90 is ...Eq 2 substitute for d into eq 2

0.1(3q-27)+0.25q=3.90, 0.3q-2.7+0.25q=3.90, 0.55q=3.9+2.7

0.55q=6.6, q=6.6/0.55=12 substitute q in eq 1

d=3(12)-27=9 dimes

 

Check in eq 2, 0.1d+0.25q=3.90 , 0.1(9)+0.25(12)=0.9+3.00=3.9

Check in eq 1, 9=3(12)=27=36-27=9 checks

 

Number of quarters= 12, number of dimes = 9