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John, Cindy, and Isaiah went to the store to buy school supplies. John bought 2 pens, 3 folders, and 4 notebooks for a total of [tex]$\$[/tex]20[tex]$. Cindy bought 5 folders and 5 notebooks for a total of $[/tex]\[tex]$25$[/tex]. Isaiah bought 3 pens, 1 folder, and 2 notebooks for a total of [tex]$\$[/tex]11[tex]$.

Which system of equations can be used to find the cost of each pen, $[/tex]p[tex]$, folder, $[/tex]f[tex]$, and notebook, $[/tex]n$?

A.
[tex]\[
2p + 3f + 4n = 20 \\
5f + 5n = 25 \\
3p + f + 2n = 11
\][/tex]

B.
[tex]\[
p + f + n = 20 \\
f + n = 25 \\
3p + f + 2n = 11
\][/tex]

C.
[tex]\[
2p + 3f + 4n = 25 \\
5f + 5n = 20 \\
3p + f + 2n = 11
\][/tex]

D.
[tex]\[
2p + 3f + 4n = 20 \\
5f + 2n = 11 \\
3n + f + 5n = 25
\][/tex]



Answer :

GinnyAnswer
To determine the correct system of equations that can be used to find the cost of each pen ([tex]\( p \)[/tex]), folder ([tex]\( f \)[/tex]), and notebook ([tex]\( n \)[/tex]), we'll look at the information given and match it with the choices provided.

1. John purchased:
- 2 pens ([tex]\( p \)[/tex])
- 3 folders ([tex]\( f \)[/tex])
- 4 notebooks ([tex]\( n \)[/tex])
For a total cost of \[tex]$20. This gives the equation: \( 2p + 3f + 4n = 20 \). 2. Cindy purchased: - 0 pens - 5 folders (\( f \)) - 5 notebooks (\( n \)) For a total cost of \$[/tex]25.
This gives the equation: [tex]\( 5f + 5n = 25 \)[/tex].

3. Isaiah purchased:
- 3 pens ([tex]\( p \)[/tex])
- 1 folder ([tex]\( f \)[/tex])
- 2 notebooks ([tex]\( n \)[/tex])
For a total cost of \$11.
This gives the equation: [tex]\( 3p + f + 2n = 11 \)[/tex].

Now, let's compare these equations with the provided options:

Option A:
[tex]\[ \begin{array}{r} 2 p+3 f+4 n=20 \\ 5 f+5 n=25 \\ 3 p+f+2 n=11 \end{array} \][/tex]

This configuration matches our derived equations exactly:
- [tex]\( 2p + 3f + 4n = 20 \)[/tex]
- [tex]\( 5f + 5n = 25 \)[/tex]
- [tex]\( 3p + f + 2n = 11 \)[/tex]

Option B:
[tex]\[ \begin{array}{r} p+f+n=20 \\ f+n=25 \\ 3 p+f+2 n=11 \end{array} \][/tex]

This configuration does not match our equations. The first equation should equal 20, not the individual items summing to 20. So, this is incorrect.

Option C:
[tex]\[ \begin{array}{r} 2 p+3 f+4 n=25 \\ 5 f+5 n=20 \\ 3 p+f+2 n=11 \end{array} \][/tex]

This is also incorrect. The totals for the first and second equations are incorrect; they have been swapped.

Option D:
[tex]\[ \begin{array}{r} 2 p+3 f+4 n=20 \\ 5 f+2 n=11 \\ 3 n+f+5 n=25 \end{array} \][/tex]

This configuration is incorrect. The second and third equations do not match any of our derived equations.

Thus, the correct answer is:

A.
[tex]\[ \begin{array}{r} 2 p+3 f+4 n=20 \\ 5 f+5 n=25 \\ 3 p+f+2 n=11 \end{array} \][/tex]

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