Question

A boy has 11 coins in dimes and quarters. Their value is $1.70. How many of each does he have? Which of the following equations could be used to solve the problem? x + (11 - x) = 1.70 25x + 10(11 - x) = 1.70 0.10x + 0.25(11 - x) = 1.70

Answer 1

Translate the statements into equations. We can use 'x' for dimes and 'y' for quarters.

"A boy has 11 coins in dimes and quarters"

$\sf x+y=11$

"Their value is $1.70"

$\sf 0.10x+0.25y=1.70$

To solve this, we can first solve for one of the variables in the first equation, and then plug that into the second equation:

$\sf x+y=11$

Subtract 'x' to both sides:

$\sf y=11-x$

Now plug this value of 'y' into the second equation:

$\boxed{\sf 0.10x+0.25(11-x)=1.70}$

So this equation could be used to solve the problem.

Answer 2

0.10x + 0.25(11 - x) = 1.70