Question 1091589

Carlos has a box of coins that he uses when playing poker with friends. The box currently contains 39 ​coins, consisting of​ pennies, dimes, and quarters. The number of pennies is equal to the number of​ dimes, and the total value is ​$3.90. How many of each denomination of coin does he​ have?
<pre>Let number of dimes be D, and quarters, Q
Then number of pennies also = D
We then get: D + D + Q = 39______2D + Q = 39_____Q = 39 - 2D ------ eq (i)
Also, .01D + .1D + .25Q = 3.9_____.11D + .25Q = 3.9_____-eq (ii)
.11D + .25(39 - 2D) = 3.9 ------ Substituting 39 - 2D for Q in eq (ii)
.11D + 9.75 - .5D = 3.9
.11D - .5D = 3.9 - 9.75
- .39D = - 5.85
D, or number of dimes/number of pennies = {{{highlight_green(matrix(1,3, (- 5.85)/(- .39), "=", 15))}}}
Number of quarters: {{{highlight_green(matrix(1,5, 39 - 2(15), "=", 39 - 30, "=", 9))}}}