Sally has a total of 40 quarters and dimes worth $6.55. How many of each does she have?

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Answer 1 · 2016-12-04T15:41:19

Sally has 23 dimes worth $2.30 and 17 quarters worth $4.25

Let's call the number of dimes Sally has #d# and the number of quarters Sally has #q#.

We can then write these two equations from the information given in the problem:

#d + q = 40#

#0.1d + .025q = 6.55#

Step 1) Solve the first equation for #d#:

#d + q - q = 40 - q#

#d + 0 = 40 - q#

#d = 40 - q#

Step 2) Substitute #40 - q# for #d# in the second equation and solve for #q#:

#0.1(40 - q) + 0.25q = 6.55#

#4 - 0.1q + 0.25q = 6.55#

#4 + 0.15q = 6.55#

#4 - 4 + 0.15q = 6.55 - 4#

#0 + 0.15q = 2.55#

#0.15q = 2.55#

#(0.15q)/0.15 = 2.55/0.15#

#q = 17#

Step 3) Substitute #17# for #q# into the solution to the first equation in Step 1) and calculate #d#;

#d = 40 - 17#

#d = 23#