Question 7:

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


responses
40
218
20
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Answer 1

To find the minimum number of lawns that Elliot needs to mow, we can set up the inequality based on his earnings.

Elliot already has $40 and earns $20 for every lawn he mows, and he needs at least $218 to buy the bike. Let \( x \) represent the number of lawns he mows. The total money he will have can be expressed as:

\[ 40 + 20x \]

We want this amount to be at least $218, so we set up the inequality:

\[ 40 + 20x \geq 218 \]

Part 1: Write the Inequality

The inequality that Elliot can use to show the minimum amount of lawns he needs to mow is:

\[ 40 + 20x \geq 218 \]

Part 2: Solve the Inequality

Now, let's solve the inequality:

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 he can't mow a fraction of a lawn, we round up to the nearest whole number. Thus, he needs to mow at least 9 lawns.

Final Answer

The inequality that represents the minimum number of lawns he needs to mow is:

\[ x \geq 9 \]