Question

Riley and Erik have earned a total of 135 tokens to buy items in the school store. The ratio of the number of tokens that Riley had to the number of tokens that Erik has is 8 to 7. How many tokens does Riley have?

Answer 1

Answer:

Riley has 72 tokens

Step-by-step explanation:

System of Equations

We have two conditions for the tokens Riley and Erik have earned. Let's call x and y to the number of tokens of Riley and Erik respectively. The first condition states that

$x+y=135$

Solving for y

$y=135-x$

The second condition is that the ratio of the number of tokens that Riley had to the number of tokens that Erik has is 8 to 7. It's written as

$\displaystyle \frac{x}{y}=\frac{8}{7}$

Or equivalently

$7x=8y$

Replacing y from the first equation

$7x=8(135-x)$

Operating

$7x=1080-8x$

Simplifying

$15x=1080$

$\boxed{x=72}$

Riley has 72 tokens