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#