Question 1

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
+

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)
x


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Answer 1

To start, let's write the inequality that represents the situation. Elliot needs at least $218 to buy the bike, and he has already earned $40. He will earn $20 for each lawn he mows.

We can set up the inequality based on his earnings:

\[ 20x + 40 \geq 218 \]

Here, \( x \) represents the number of lawns he mows.

Now, we'll solve the inequality to find the minimum number of lawns 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 and must be a whole number, we round up to the nearest whole number:

\[ x \geq 9 \]

So, Elliot needs to mow a minimum of 9 lawns to buy the new BMX bike.

To summarize:

• The inequality he can use is:
  \( 20x + 40 \geq 218 \)

• The solution to the inequality shows that he must mow at least 9 lawns.