# Kendra has $6.00 in dimes and quarters. If she has 2 times as many quarters as dimes, how many of each coin does she have?

Make a system of equations. [latex]\sf0.10d+0.25q=6[/latex] [latex]\sf~q = 2d[/latex] Plug in 2d for 'q' in the first equation: [latex]\sf0.10d+0.25q=6[/latex] [latex]\sf0.10d+0.25(2d)=6[/latex] Multiply: [latex]\sf0.10d+0.50d=6[/latex] Combine like terms: [latex]\sf0.60d=6[/latex] Divide 0.60 to both sides: [latex]\sf~d=10[/latex] Now plug this into any of the two equations to find 'q': [latex]\sf~q = 2d[/latex] [latex]\sf~q = 2(10)[/latex] [latex]\sf~q = 20[/latex] So she has 10 dimes and 20 quarters.

.10x = dimes ----------\ + 6.00 2(.25x) = quarters---/ .10x + 2(.25x) =6.00 .10(10) + 2(.25(10)) =6.00 10x + 50x = 600 1 + 2(2.50) = 6.00 60x = 600 1+ 5.00 = 6.00 x = 10 6.00 = 6.00