Question

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)

218

<

40
x
+

20
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 find the minimum number of lawns Elliot needs to mow, we start with the cost of the BMX bike, which is $218. He has already earned $40 from mowing lawns. He makes $20 for each lawn he mows, which we need to represent with the variable \( x \).

The inequality representing how much money he will have after mowing \( x \) lawns is:

\[
20x + 40 \geq 218
\]

Now, we will solve this inequality to determine the minimum number of lawns \( x \) that he needs to mow.

1. Subtract 40 from both sides:

\[
20x \geq 218 - 40
\]

\[
20x \geq 178
\]

2. Divide both sides by 20:

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

\[
x \geq 8.9
\]

Since \( x \) represents the number of lawns he can mow, we need to round up to the next whole number because he cannot mow a fraction of a lawn. Therefore, the minimum number of lawns he needs to mow is:

\[
x \geq 9
\]

Thus, the inequality that represents the minimum number of lawns Elliot needs to mow is:

\[
x \geq 9
\]