Let's set up the equations we know. Q+D=100, where Q=number of quarters, and D=number of dimes .25Q + .1D = 21.40 (because a quarter is worth .25 and a dime worth .10)
Using the first equation, let's isolate one of our variables. I'll pick Q. Q+D=100 Subtract D from each side Q=100 - D
Now that we have this new equation, let's plug it into our second equation. .25Q + .1D = 21.40 .25(100-D) + .1D = 21.40 Distribute the .25 25 - .25D + .1 D = 21.40 Combine like terms 25 - .15D = 21.40 Subtract 21.40 from each side 3.6 - .15D = 0 Add .15 D to each side 3.6 = .15D Divide each side by .15 D = 24
Now that we have D, we can solve for Q Q= 100 - D = 100 - 24 Q = 76
Sue has 24 dimes and 76 quarters.
Let's check our work to make sure. .25(76) + .1(24) = 19 + 2.4 = 21.4 √
