Question
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Question
How would you create a multistep linear equation to represent a real-world scenario where ABC Electronics sells printers for $35 profit each and routers for $18 profit each, with a total of 125 items sold for $2,420 profit? (1 point)
Responses
35x + 18x = 2,420
35x + 18x = 2,420
35x - 18x = 2,420
35x - 18x = 2,420
35x + 18(125 - x) = 2,420
35x + 18(125 - x) = 2,420
35(125) + 18x = 2,420
Answers
GPT-4o mini
To create a multistep linear equation representing the scenario, we need to define variables for the number of printers and routers sold. Let's define:
- \( x \) = the number of printers sold
- \( y \) = the number of routers sold
From the problem statement, we know two things:
1. The total number of items sold (printers + routers) is 125:
\[
x + y = 125
\]
2. The total profit from selling these items is $2,420:
\[
35x + 18y = 2,420
\]
To express the second equation in terms of a single variable, we can substitute \( y \) from the first equation into the second.
From \( x + y = 125 \), we can express \( y \) as:
\[
y = 125 - x
\]
Substituting \( y \) into the profit equation:
\[
35x + 18(125 - x) = 2,420
\]
This is the correct multistep linear equation that captures the scenario. Therefore, the best choice from the given options is:
**35x + 18(125 - x) = 2,420**
- \( x \) = the number of printers sold
- \( y \) = the number of routers sold
From the problem statement, we know two things:
1. The total number of items sold (printers + routers) is 125:
\[
x + y = 125
\]
2. The total profit from selling these items is $2,420:
\[
35x + 18y = 2,420
\]
To express the second equation in terms of a single variable, we can substitute \( y \) from the first equation into the second.
From \( x + y = 125 \), we can express \( y \) as:
\[
y = 125 - x
\]
Substituting \( y \) into the profit equation:
\[
35x + 18(125 - x) = 2,420
\]
This is the correct multistep linear equation that captures the scenario. Therefore, the best choice from the given options is:
**35x + 18(125 - x) = 2,420**