Roxanne's Coins
32) Roxanne had 39 coins (quarters and dimes) that totaled $7.80. How many
of each coin did she have?
x = quarters
y = dimes
x + y = 39 (Our first equation deals with the number of coins.)
25x + 10y = 780 (These amounts are in pennies.)
-10x -10y = -390 (We multiplied the top equation by -10, so that
we'll be able to cancel out a variable when adding.)
-10x -10y = -390
25x +10y = 780
---------------
15x = 390
x = 26 (We divided both sides by 15 to find the value of x.)
We will now plug the value of x (26) into the equation above to
determine the value of y:
26 + y = 39
y = 13 (We subtracted 26 from both sides to isolate the variable
y on one side of the equal sign and see its value on the
other.)
Now that we know the value for both variables, we can double-check
our work:
26 quarters = $6.50
13 dimes = $1.30
-------------------
39 coins $7.80