# A cell phone company offers text message plans where the number of texts allowed varies directly with the amount of money paid. Their most popular plan is 400 texts for $8. How many text messages are included in the plan that costs$10? 500, 600, 700, 800

Jun 23, 2018

$500$

#### Explanation:

Since the amount of text messages varies directly with the amount of money paid, it will be proportional.

So set up a proportion:

$\text{number of text messages"/"amount of money}$ $= \frac{400}{8}$

The second plan will be proportional to the first one, so here is the resulting equation:

$\frac{400}{8} = \frac{x}{10}$

The number of text messages in the second plan is not known, so I gave it the variable $x$. However, the amount of money is known.

Now cross multiply to solve:

$\frac{400}{8} = \frac{x}{10}$

$\frac{400}{8} = \frac{x}{10}$

$400 \times 10 = x \times 8$

$4000 = 8 x$

$500 = x$

So the amount of messages included in the second plan is $500$