Question

On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"?

Answer 1

Lorenzo gets 4 points for each x and 8 points for each y and needs at least 50 points to get a B so:

4x+8y≥50 which can be simplified by factoring out 2 from the inequality

2x+4y≥25

Answer 2

`2x+4y\leq 25`

Explanation:

Number of points scored for each multiple choice question = 4 points

Number of points scored for word problem = 8 points

Let x denotes number of correct multiple choice questions and y denotes number of correct word problems.

So,

Total points scored for correct multiple choice question = 4x

Total points scored for correct word problems = 8y

Number of points required by Lorenzo to earn B in class = Atleast 50 points

According to question,

Total points scored for correct multiple choice question + Total points scored for correct word problems
`\leq` 50

`4x+8y\leq 50`

On taking 2 common, we get
`2x+4y\leq 25`