Question
The school band is ordering health bars to sell for a fundraiser. The company that sells the bars charges $0.40 per bar plus $20.00 for shipping regardless of the size of the order. The band must spend less than $200.00 on bars for the fundraiser. The inequality below relates x, the number of bars that could be ordered, with the shipping costs and their spending requirements.
0.40 x + 20 less-than 200
Which best describes the number of bars the band can order?
They can order from 0 to 449 bars, but no more.
They can order from 0 to 450 bars, but no more.
Their order must contain 451 bars or more.
Their order must contain 452 bars or more.
0.40 x + 20 less-than 200
Which best describes the number of bars the band can order?
They can order from 0 to 449 bars, but no more.
They can order from 0 to 450 bars, but no more.
Their order must contain 451 bars or more.
Their order must contain 452 bars or more.
Answers
Answered by
GPT-4o mini
To solve the inequality \( 0.40x + 20 < 200 \), we will first isolate \( x \).
1. Subtract 20 from both sides:
\[
0.40x < 200 - 20
\]
\[
0.40x < 180
\]
2. Now, divide both sides by 0.40:
\[
x < \frac{180}{0.40}
\]
\[
x < 450
\]
This result tells us that the number of bars \( x \) can be less than 450.
Since the number of bars must be a non-negative integer, the possible values for \( x \) range from 0 to 449.
Therefore, the best description of the number of bars the band can order is:
- **They can order from 0 to 449 bars, but no more.**
1. Subtract 20 from both sides:
\[
0.40x < 200 - 20
\]
\[
0.40x < 180
\]
2. Now, divide both sides by 0.40:
\[
x < \frac{180}{0.40}
\]
\[
x < 450
\]
This result tells us that the number of bars \( x \) can be less than 450.
Since the number of bars must be a non-negative integer, the possible values for \( x \) range from 0 to 449.
Therefore, the best description of the number of bars the band can order is:
- **They can order from 0 to 449 bars, but no more.**