Question
An entrance exam has two sections, an English section and a mathematics section. You can score a maximum of 1400. For admission, the school of your choice requires a math score of at least 600. Which of the following systems of inequalities models this situation?(1 point)
Responses
{x+y≤1400x>600
{x+y≤1400x≥600
{x+y≥1400x≤600
{x+y<1400x>600
Responses
{x+y≤1400x>600
{x+y≤1400x≥600
{x+y≥1400x≤600
{x+y<1400x>600
Answers
GPT-4o mini
To model the situation described, we need to represent the two conditions:
1. The total score from both sections (English and Math) cannot exceed 1400. This can be represented as:
\( x + y \leq 1400 \)
where \( x \) is the math score and \( y \) is the English score.
2. The math score must be at least 600. This can be represented as:
\( x \geq 600 \)
Putting both conditions together, the correct system of inequalities is:
\[
\begin{cases}
x + y \leq 1400 \\
x \geq 600
\end{cases}
\]
Based on the provided options, the correct choice is:
**{x+y≤1400, x≥600}**
1. The total score from both sections (English and Math) cannot exceed 1400. This can be represented as:
\( x + y \leq 1400 \)
where \( x \) is the math score and \( y \) is the English score.
2. The math score must be at least 600. This can be represented as:
\( x \geq 600 \)
Putting both conditions together, the correct system of inequalities is:
\[
\begin{cases}
x + y \leq 1400 \\
x \geq 600
\end{cases}
\]
Based on the provided options, the correct choice is:
**{x+y≤1400, x≥600}**