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Answer :
To solve the problem of determining the number of [tex]$10.00 DVDs and $[/tex]15.00 DVDs in a box, we can set up a system of equations based on the given information. Here's a detailed breakdown:
1. Define Variables:
- Let [tex]\( x \)[/tex] be the number of DVDs worth [tex]$10 each.
- Let \( y \) be the number of DVDs worth $[/tex]15 each.
2. Establish Equations:
- First, we consider the total number of DVDs in the box. The problem states there are 14 DVDs in total. This gives us the equation:
[tex]\[
x + y = 14
\][/tex]
- Next, we consider the total value of these DVDs. The problem states that the total value is [tex]$170. Since each $[/tex]10 DVD contributes [tex]$10 and each $[/tex]15 DVD contributes [tex]$15 to the total, we can write the equation:
\[
10x + 15y = 170
\]
3. System of Equations:
- We now have a system of two equations:
\[
\begin{cases}
x + y = 14 \\
10x + 15y = 170
\end{cases}
\]
4. Matching the System to Options:
- Option A lists the system \( 10x + 15y = 170 \) and \( x + y = 14 \), which matches our system of equations.
Thus, the correct system of equations to determine the number of $[/tex]10.00 DVDs and $15.00 DVDs is:
Option A:
[tex]\[
10x + 15y = 170 \\
x + y = 14
\][/tex]
1. Define Variables:
- Let [tex]\( x \)[/tex] be the number of DVDs worth [tex]$10 each.
- Let \( y \) be the number of DVDs worth $[/tex]15 each.
2. Establish Equations:
- First, we consider the total number of DVDs in the box. The problem states there are 14 DVDs in total. This gives us the equation:
[tex]\[
x + y = 14
\][/tex]
- Next, we consider the total value of these DVDs. The problem states that the total value is [tex]$170. Since each $[/tex]10 DVD contributes [tex]$10 and each $[/tex]15 DVD contributes [tex]$15 to the total, we can write the equation:
\[
10x + 15y = 170
\]
3. System of Equations:
- We now have a system of two equations:
\[
\begin{cases}
x + y = 14 \\
10x + 15y = 170
\end{cases}
\]
4. Matching the System to Options:
- Option A lists the system \( 10x + 15y = 170 \) and \( x + y = 14 \), which matches our system of equations.
Thus, the correct system of equations to determine the number of $[/tex]10.00 DVDs and $15.00 DVDs is:
Option A:
[tex]\[
10x + 15y = 170 \\
x + y = 14
\][/tex]
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