A woman has 26 coins in her pocket, all of which are dimes and quarters. If the total value of the coins is $ 5.45, how many dimes and how many quarters does she have?
+128474 Let the number of dimes = x
Let the number of quarters = 26 -x
And
Number of dimes * Value of each + Number of quarters * value each = total value of the coins
So...
x * .10 + (26 - x) * .25 = 5.45 simplify
.10x - .25x + 6.50 = 5.45 subtract 6.50 from both sides and simplify the left side
-.15x = -1.05 divide both sides by -.15
x = 7 = number of dimes
26 - x = 26 - 7 = 19 = number of quarters
