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Question 7:

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)



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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)
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1 answer

To find out how many lawns Elliot needs to mow to afford the BMX bike, we can start by setting up the inequality.

Step 1: Write the Inequality

The total amount of money Elliot will have after mowing \( x \) lawns is $40 (what he has already earned) plus $20 for each lawn he mows:

\[ 40 + 20x \geq 218 \]

Step 2: Solve the Inequality

Now, we'll solve the inequality for \( x \).

  1. Subtract 40 from both sides:

\[ 20x \geq 218 - 40 \]

\[ 20x \geq 178 \]

  1. Divide both sides by 20:

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

\[ x \geq 8.9 \]

Since \( x \) represents the number of lawns, and he can't mow a fraction of a lawn, we round up to the nearest whole number:

\[ x \geq 9 \]

Final Answer

Elliot needs to mow at least 9 lawns to earn enough money to buy the BMX bike.

The two parts are:

  1. The inequality used: \( 40 + 20x \geq 218 \)
  2. The minimum number of lawns he needs to mow: \( x \geq 9 \)