I have eight more quarters than dimes. If the coins are worth $6.20 how many dimes are there?

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Answer 1 · 2016-10-30T21:25:04

20 quarters and 12 dimes.

0.25 = 1/4

0.10 = 1/10

$n_1$ = number of quarters

$n_2$ = number of dimes

Equation 1:

$n_1*1/4+n_2*1/10=62/10$

Equation 2:

$n_1=n_2+8$

$n_2+8$ plugged into equation 1:

$(n_2+8)*1/4+n_2*1/10=62/10$

$n_2*1/4+2+n_2*1/10=62/10$

$n_2(1/4+1/10)+2=62/10$

$n_2(5/20+2/20)=62/10-20/10$

$7/20*n_2=42/10$

$7/20*n_2=84/20$

$7n_2=84$

$n_2=12$

If $n_2=12$ :

$n_1=12+8$

$n_1=20$

This means that there are 20 quarters and 12 dimes . Now, let's just see if this is in fact correct:

$20*1/4+12*1/10$

$=5+1.2$

$=6.2$