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 _____. A. 8.5x + 20 > 54 B. 8.5x - 20 < 54 C. 54 - 8.5x < 20 D. 54 - 8.5x > 20

The number of tubes of paint Catherine can buy is _____. A. at least 5 B. more than 4 C. less than 4 D. more than 5

Answer 1

The answer is B. She is buying 4 paint tubes. 4 x 8.5 = 34. 34 - 20 = 14, which is less than 54.

Answer 2

Step 1

Let

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

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

we know that

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

$y=54-8.5x$ ------> equation B

substitute equation B in inequality A

$54-8.5x > 20$

therefore

the answer part a) is

The inequality that best represents this scenario is $54-8.5x > 20$

Step 2

Solve the inequality

$54-8.5x > 20$

$54-20 >8.5x$

$34 >8.5x$

$34/8.5 >x$

$4 >x$ ---------> $x < 4$

therefore

the answer Part b) is the option C

less than $4$