Thomas has a collection of 25 coins some are dimes and some are quarters. If the total value of all the coins is $5.05, how many of each kind of coin are there?

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Answer 1 · 2016-11-24T12:11:30

Thomas has 8 dimes and 17 quarters

To start, let's call the number of dimes Thomas has #d# and the number of quarters he has #q#.

Then, because we know he has 25 coins we can write:

#d + q = 25#

We also know the combination of dimes and quarters add up to #$5.05# so we can also write:

#0.10d + 0.25q = 5.05#

Solving the first equation for #q# gives:

#d + q - d = 25 - d#

#q = 25 - d#

We can now substitute #25 - d# for #q# in the second equation and solve for #d#:

#0.10d + 0.25(25 - d) = 5.05#

#0.10d + 6.25 - 0.25d = 5.05#

#6.25 - 0.15d = 5.05#

#6.25 - 0.15d + 0.15d - 5.05 = 5.05 + 0.15d - 5.05#

#1.20 = 0.15d#

#1.20/0.15 = (0.15d)/0.15#

#d = 8#

We can now substitute #8# for #d# in the solution of the first equation and calculate #q#.

#q = 25 - 8#

#q = 17#