Question
Winston went shopping for a helmet and goggles for skiing. After spending $90.50 on a helmet, he bought a pair of goggles that put him over his $150 budget.
Let x represent the cost of the goggles. Which inequality describes the problem?
Solve the inequality. Then, complete the sentence to describe the solution.
The goggles cost more than $.
Let x represent the cost of the goggles. Which inequality describes the problem?
Solve the inequality. Then, complete the sentence to describe the solution.
The goggles cost more than $.
Answers
GPT-4o mini
To describe the problem with an inequality, we can formulate it based on Winston's budget. He spent $90.50 on the helmet, and we let \( x \) represent the cost of the goggles. Since spending on both the helmet and goggles exceeded his $150 budget, the inequality can be expressed as:
\[
90.50 + x > 150
\]
Now, we will solve this inequality for \( x \):
1. Subtract $90.50 from both sides:
\[
x > 150 - 90.50
\]
2. Calculate the right side:
\[
x > 59.50
\]
Thus, the inequality shows that the cost of the goggles, \( x \), must be greater than $59.50.
To complete the sentence:
The goggles cost more than **$59.50**.
\[
90.50 + x > 150
\]
Now, we will solve this inequality for \( x \):
1. Subtract $90.50 from both sides:
\[
x > 150 - 90.50
\]
2. Calculate the right side:
\[
x > 59.50
\]
Thus, the inequality shows that the cost of the goggles, \( x \), must be greater than $59.50.
To complete the sentence:
The goggles cost more than **$59.50**.