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
Answers
GPT-4o mini
To create an inequality that shows the minimum number of lawns Elliot needs to mow to earn at least enough money to buy the BMX bike, we start with the total cost of the bike and how much he already has.
1. The cost of the bike is $218.
2. Elliot has already earned $40.
3. For every lawn he mows, he earns $20, so if \( x \) represents the number of lawns he mows, his earnings from mowing will be \( 20x \).
The total amount of money he will have after mowing \( x \) lawns will be the money he already has plus the money he will earn from mowing:
\[
40 + 20x
\]
We want this amount to be at least $218, which leads us to the following inequality:
\[
40 + 20x \geq 218
\]
### Next, we 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 \( x \) must be a whole number (he can't mow a fraction of a lawn), we round up to the nearest whole number:
\[
x \geq 9
\]
### Conclusion:
Elliot needs to mow **at least 9 lawns** to earn enough money to buy the BMX bike.
### Final Answer:
1. The inequality is: \( 40 + 20x \geq 218 \).
2. The minimum number of lawns he needs to mow is \( x \geq 9 \).
1. The cost of the bike is $218.
2. Elliot has already earned $40.
3. For every lawn he mows, he earns $20, so if \( x \) represents the number of lawns he mows, his earnings from mowing will be \( 20x \).
The total amount of money he will have after mowing \( x \) lawns will be the money he already has plus the money he will earn from mowing:
\[
40 + 20x
\]
We want this amount to be at least $218, which leads us to the following inequality:
\[
40 + 20x \geq 218
\]
### Next, we 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 \( x \) must be a whole number (he can't mow a fraction of a lawn), we round up to the nearest whole number:
\[
x \geq 9
\]
### Conclusion:
Elliot needs to mow **at least 9 lawns** to earn enough money to buy the BMX bike.
### Final Answer:
1. The inequality is: \( 40 + 20x \geq 218 \).
2. The minimum number of lawns he needs to mow is \( x \geq 9 \).