Brayton has a goal of saving more than $350 this week. He earns $20 for each kid he tutors after school. This week it also happened to be his birthday, and he received $100 as a gift for his birthday. Write and solve an inequality for the number of kids Brayton needs to tutor this week. Which answer choice best interprets the solution in the context of the problem?(1 point)

Question

Responses

Brayton needs to tutor at least 13 kids this week to meet his goal.
Brayton needs to tutor at least 13 kids this week to meet his goal.

Brayton needs to tutor at least 13 hours to meet his goal.
Brayton needs to tutor at least 13 hours to meet his goal.

Brayton needs to tutor 12.5 kids to meet his goal.
Brayton needs to tutor 12.5 kids to meet his goal.

Brayton needs to tutor more than 12.5 hours to meet his goal.

Answer 1

To model Brayton's savings goal as an inequality, we first need to consider his earnings from tutoring and his birthday gift.

1. Let \( x \) be the number of kids Brayton tutors.
2. He earns $20 for each kid he tutors, so his total earnings from tutoring can be represented as \( 20x \).
3. He received $100 as a birthday gift, which adds to his total savings.
4. He wants to save more than $350, so we can write the inequality:

\[ 20x + 100 > 350 \]

Next, we solve the inequality:

1. Subtract 100 from both sides:

\[ 20x > 250 \]

2. Divide both sides by 20:

\[ x > 12.5 \]

Since \( x \) must represent a whole number of kids, Brayton needs to tutor at least 13 kids.

Now, we analyze the response choices:

1. "Brayton needs to tutor at least 13 kids this week to meet his goal." (This is true.)
2. "Brayton needs to tutor at least 13 hours to meet his goal." (This is incorrect, as we deal with kids, not hours.)
3. "Brayton needs to tutor 12.5 kids to meet his goal." (This is incorrect, as he needs more than 12.5.)
4. "Brayton needs to tutor more than 12.5 hours to meet his goal." (This is incorrect, as we deal with kids, not hours.)

The best interpretation of the solution is:

Brayton needs to tutor at least 13 kids this week to meet his goal.