Question

Catherine has $54. She plans to spend more than $20 of the money for a painting canvas. The rest will go toward paints. Each tube of paint costs $8.50. Assume that x represents the number of tubes of paint Catherine can buy. The inequality that best represents this scenario is . The number of tubes of paint Catherine can buy is .

The inequality that best represents this scenario is =????
The number of tubes of paint Catherine can buy is=??

Answer 1

x-------> represents the number of tubes of paint Catherine can buy

y------> the money to spend for a painting canvas

we know that

y > 20y>20 ------> inequality A

y=54-8.5xy=54−8.5x ------> equation B

substitute equation B in inequality A

54-8.5x > 2054−8.5x>20

therefore

Answer 2

There is a fixed cost of $20 at the beginning, then each of the x tubes of paint costs $8.50. This means that all the tubes of paint will cost 8.5x. The total cost (including the canvas) will be 20 + 8.5x. The maximum amount is 54, so the inequality is:
20 + 8.5x <= 54
Solving gives:
8.5x <= 34
x <= 4
So the maximum number of tubes of paint is 4.