Derrick wants some new sneakers. The ones he is hoping for cost $142.25, so he needs at least $142.25. If he can get more than $142.25, that would be even better because he wants to get some new shoelaces and other clothes, too, if possible. He has $35 save already. He decides to mow lawns in his neighborhood to earn more money. He can make $15 for each lawn he mows. Write and solve an inequality that represents the number of lawns Derrick needs to mow before heading to the store. Interpret your answer in the context of the problem.

Question

All I have right now is this:
Goal: $142.25
Savings: $35.00
How much he gets for each lawn he mows: $15.00
How much he needs: $107.25

GPT-4o mini · Answer

To solve the problem, we'll first establish what Derrick needs and how much he can earn by mowing lawns.

Calculate the amount Derrick still needs after his savings: \[ \text{Amount needed} = \text{Cost of sneakers} - \text{Current savings} = 142.25 - 35 = 107.25 \]
Define the variables: Let $x$ be the number of lawns Derrick mows. Since he earns $15 for each lawn, his total earnings from mowing $x$ lawns will be $15x$.
Set up the inequality: To find out how many lawns Derrick needs to mow in order to have at least enough for the sneakers, we can set up the following inequality: \[ 15x + 35 \geq 142.25 \]
Solve the inequality: First, isolate $15x$: \[ 15x \geq 142.25 - 35 \] \[ 15x \geq 107.25 \]

Next, divide both sides by 15: \[ x \geq \frac{107.25}{15} \] \[ x \geq 7.15 \]

Since Derrick cannot mow a fraction of a lawn, we round up to the nearest whole number: \[ x \geq 8 \]
Interpretation: Derrick needs to mow at least 8 lawns to have enough money to buy the sneakers. Mowing 8 lawns will give him: \[ 15 \times 8 + 35 = 120 + 35 = 155 \] This total of $155 not only covers the cost of the sneakers ($142.25) but also provides him with additional funds for shoelaces and other clothes. Thus, he should aim to mow at least 8 lawns before heading to the store.

Xye · Answer

Oh! okay, thanks, GPT-4o mini :)