Isaac is going to an art store. He buys one can of paint for $22, and spends the rest of his money on paintbrushes that cost $7 each. How many paintbrushes can Isaac buy if he has exactly $85 to spend?

Question

Let p be the number of paintbrushes Isaac buys. Start by writing an expression that represents the amount of money Isaac spends at the art store.

Answer 1

First, we need to calculate how much money Isaac has left after buying one can of paint for $22. He starts with $85, so after the purchase of the paint, the amount of money he has left is:

\[ 85 - 22 = 63 \text{ dollars} \]

Now, let \( p \) represent the number of paintbrushes that Isaac buys. Each paintbrush costs $7, so the total amount of money spent on paintbrushes can be represented as:

\[ 7p \]

To find the total amount of money Isaac spends at the art store, we can combine the cost of the paint and the cost of the paintbrushes:

\[ \text{Total amount spent} = \text{Cost of paint} + \text{Cost of paintbrushes} = 22 + 7p \]

Since we know he can spend up to $85, we can express this relationship as:

\[ 22 + 7p \leq 85 \]

This expression represents the total amount of money Isaac spends at the art store.