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

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.

Answer 2

.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