# 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? ##### 1 Answer Nov 24, 2016 Thomas has 8 dimes and 17 quarters #### Explanation: 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:

$0.10 d + 0.25 q = 5.05$

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 $d$:

$0.10 d + 0.25 \left(25 - d\right) = 5.05$

$0.10 d + 6.25 - 0.25 d = 5.05$

$6.25 - 0.15 d = 5.05$

$6.25 - 0.15 d + 0.15 d - 5.05 = 5.05 + 0.15 d - 5.05$

$1.20 = 0.15 d$

$\frac{1.20}{0.15} = \frac{0.15 d}{0.15}$

$d = 8$

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

$q = 25 - 8$

$q = 17$