Question

Elliot wants to buy a new BMX bike which costs $218. He plans to mow lawns this summer so that he can earn at least enough money to buy the bike. He will earn $20 for every lawn that he mows, and he has already made $40. Write an inequality that can he use to show the minimum amount of lawns he needs to mow, where x represents the number of lawns.

(5 points)



x

Question 2
Solve the inequality you wrote, and create the inequality that represents the minimum number of lawns you determined he needs to mow to buy the new BMX bike. (2 points)
x

Answer 1

To determine the minimum amount of lawns Elliot needs to mow, we can set up an inequality based on the information given.

**Step 1: Write the inequality.**

Elliot needs to have at least $218. He has already earned $40 and will earn $20 for every lawn he mows. Let \( x \) represent the number of lawns he mows.

The total amount of money he will have after mowing \( x \) lawns is given by:

\[
40 + 20x
\]

To ensure this amount is at least $218, we write the inequality:

\[
40 + 20x \geq 218
\]

**Step 2: Solve the inequality.**

Let's solve for \( x \):

1. Subtract 40 from both sides:

\[
20x \geq 218 - 40
\]

\[
20x \geq 178
\]

2. Now, divide by 20:

\[
x \geq \frac{178}{20}
\]

\[
x \geq 8.9
\]

Since \( x \) represents the number of lawns, it needs to be a whole number. Therefore, we round up to the nearest whole number:

\[
x \geq 9
\]

**Final Answer:**

**Question 1:**
The inequality is:
\[
40 + 20x \geq 218
\]

**Question 2:**
The solution gives us the minimum number of lawns he needs to mow, which is:
\[
x \geq 9
\]

Elliot needs to mow at least **9 lawns** to buy the BMX bike.