Question
A sports team is selling handmade art and jewelry to raise money for new uniforms. They charged $15 for each art piece and $10 for each piece of jewelry, selling a maximum of 75 pieces of art and jewelry combined. Their goal is to raise at least $1,000. Which of the following systems of inequalities represents this scenario, if a is the amount of art pieces and j is the amount of jewelry pieces sold?(1 point)
Responses
a+j≤75
15a+10j≤1,000
a plus j less-than-or-equal-to 75 15 a plus 10 j less-than-or-equal-to 1,000
a+j≤75
15a+10j≥1,000
a plus j less-than-or-equal-to 75 15 a plus 10 j greater-than-or-equal-to 1,000
a+j≤1,000
15a+10j≥75
a plus j less-than-or-equal-to 1,000 15 a plus 10 j greater-than-or-equal-to 75
a+j≥75
15a+10j≥1,000
a plus j greater-than-or-equal-to 75 15 a plus 10 j greater-than-or-equal-to 1,000
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Responses
a+j≤75
15a+10j≤1,000
a plus j less-than-or-equal-to 75 15 a plus 10 j less-than-or-equal-to 1,000
a+j≤75
15a+10j≥1,000
a plus j less-than-or-equal-to 75 15 a plus 10 j greater-than-or-equal-to 1,000
a+j≤1,000
15a+10j≥75
a plus j less-than-or-equal-to 1,000 15 a plus 10 j greater-than-or-equal-to 75
a+j≥75
15a+10j≥1,000
a plus j greater-than-or-equal-to 75 15 a plus 10 j greater-than-or-equal-to 1,000
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Answers
GPT-4o mini
To properly represent the scenario with a system of inequalities, we can consider the following information:
1. The total amount of art pieces (a) and jewelry pieces (j) sold cannot exceed 75:
\[
a + j \leq 75
\]
2. The team aims to raise at least $1,000. The income from selling the art pieces at $15 each and the jewelry at $10 each must be at least $1,000:
\[
15a + 10j \geq 1,000
\]
From the above information, we can identify that the correct set of inequalities representing the scenario is:
\[
\begin{align*}
a + j & \leq 75 \\
15a + 10j & \geq 1,000
\end{align*}
\]
This corresponds to the option that states:
**a plus j less-than-or-equal-to 75, 15 a plus 10 j greater-than-or-equal-to 1,000**.
1. The total amount of art pieces (a) and jewelry pieces (j) sold cannot exceed 75:
\[
a + j \leq 75
\]
2. The team aims to raise at least $1,000. The income from selling the art pieces at $15 each and the jewelry at $10 each must be at least $1,000:
\[
15a + 10j \geq 1,000
\]
From the above information, we can identify that the correct set of inequalities representing the scenario is:
\[
\begin{align*}
a + j & \leq 75 \\
15a + 10j & \geq 1,000
\end{align*}
\]
This corresponds to the option that states:
**a plus j less-than-or-equal-to 75, 15 a plus 10 j greater-than-or-equal-to 1,000**.