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.

Question

(5 points)

40

≥

20
x
+

218
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)

Answer 1

To form the inequality for Elliot's situation, we need to account for how much money he needs and how much he will earn from mowing lawns.

1. Identify the total amount of money Elliot needs: The BMX bike costs $218.

2. Account for the money he has already made: Elliot has already made $40.

3. Determine how much more money he needs to earn: This is calculated as follows: \[ 218 - 40 = 178 \] So, he needs to earn at least $178 more.

4. Identify how much he earns from mowing lawns: He earns $20 for every lawn he mows. If \( x \) represents the number of lawns, he earns \( 20x \) dollars from mowing \( x \) lawns.

5. Form the inequality: He needs at least $178 from mowing lawns, so we can express this as: \[ 20x \geq 178 \]

This is the inequality that represents the minimum number of lawns he needs to mow.

Now, let's solve the inequality \( 20x \geq 178 \):

1. Divide both sides by 20: \[ x \geq \frac{178}{20} \] \[ x \geq 8.9 \]

Since \( x \) must be a whole number (as he can't mow a fraction of a lawn), we round up to the next whole number.

Thus, the minimum number of lawns he needs to mow is: \[ x \geq 9 \]

In summary, the inequality is \( 20x \geq 178 \), and Elliot needs to mow at least 9 lawns to afford the bike.