Question
Match the following equation to the correct situation.
40%(b − 21) = 40%b − 8.4
A.
An amount of chili was eaten from 40% of 8.4 less than b bowls.
B.
Last month's electricity bill was 8.4 kW-h less than 40% of this month's bill.
C.
A number of cups of coffee were thrown away by 40% of b senators during 8.4 speeches.
D.
A number of songs are available for download from 40% of b artists.
40%(b − 21) = 40%b − 8.4
A.
An amount of chili was eaten from 40% of 8.4 less than b bowls.
B.
Last month's electricity bill was 8.4 kW-h less than 40% of this month's bill.
C.
A number of cups of coffee were thrown away by 40% of b senators during 8.4 speeches.
D.
A number of songs are available for download from 40% of b artists.
Answers
GPT-4o mini
To analyze the equation \( 40\%(b - 21) = 40\%b - 8.4 \), let's start by interpreting the components of the equation.
1. The left side, \( 40\%(b - 21) \), indicates that we are taking 40% of an amount that is reduced by 21 (which can represent a decrease).
2. The right side, \( 40\%b - 8.4 \), indicates that we are taking 40% of \( b \) and subtracting 8.4 from it.
Now, let's evaluate the options:
**A. An amount of chili was eaten from 40% of 8.4 less than b bowls.**
- This option does not fit because it misuses the values and relationships present in the equation.
**B. Last month's electricity bill was 8.4 kW-h less than 40% of this month's bill.**
- This is a good candidate because it describes a situation where the current bill \( b \) minus a reduction of 21 corresponds to the reduced amount (8.4) in terms of electricity billing.
**C. A number of cups of coffee were thrown away by 40% of b senators during 8.4 speeches.**
- This doesn't match because it confuses the relationships - the cups of coffee are not linked to the percentages correctly.
**D. A number of songs are available for download from 40% of b artists.**
- While this mentions percentages, it does not capture a relationship in the equation since there is no reduction or subtraction involved.
After analyzing, **B (Last month's electricity bill was 8.4 kW-h less than 40% of this month's bill.)** is the best match for the situation described by the equation \( 40%(b - 21) = 40\% b - 8.4 \).
1. The left side, \( 40\%(b - 21) \), indicates that we are taking 40% of an amount that is reduced by 21 (which can represent a decrease).
2. The right side, \( 40\%b - 8.4 \), indicates that we are taking 40% of \( b \) and subtracting 8.4 from it.
Now, let's evaluate the options:
**A. An amount of chili was eaten from 40% of 8.4 less than b bowls.**
- This option does not fit because it misuses the values and relationships present in the equation.
**B. Last month's electricity bill was 8.4 kW-h less than 40% of this month's bill.**
- This is a good candidate because it describes a situation where the current bill \( b \) minus a reduction of 21 corresponds to the reduced amount (8.4) in terms of electricity billing.
**C. A number of cups of coffee were thrown away by 40% of b senators during 8.4 speeches.**
- This doesn't match because it confuses the relationships - the cups of coffee are not linked to the percentages correctly.
**D. A number of songs are available for download from 40% of b artists.**
- While this mentions percentages, it does not capture a relationship in the equation since there is no reduction or subtraction involved.
After analyzing, **B (Last month's electricity bill was 8.4 kW-h less than 40% of this month's bill.)** is the best match for the situation described by the equation \( 40%(b - 21) = 40\% b - 8.4 \).