Question

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?

Answer 1

.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

Answer 2

Make a system of equations.


`\sf0.10d+0.25q=6`

`\sf~q = 2d`

Plug in 2d for 'q' in the first equation:


`\sf0.10d+0.25q=6`


`\sf0.10d+0.25(2d)=6`

Multiply:


`\sf0.10d+0.50d=6`

Combine like terms:


`\sf0.60d=6`

Divide 0.60 to both sides:


`\sf~d=10`

Now plug this into any of the two equations to find 'q':


`\sf~q = 2d`


`\sf~q = 2(10)`


`\sf~q = 20`

So she has 10 dimes and 20 quarters.