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Answer :
To find the cost of one scone and one mug of chai tea, we can set up a system of linear equations based on the information given.
Let's define:
- [tex]\( x \)[/tex] as the cost of one scone.
- [tex]\( y \)[/tex] as the cost of one mug of chai tea.
From the problem, we can write the following equations based on the purchases:
1. Julianna purchased 2 scones and 3 mugs of chai tea for \[tex]$16.25. This can be represented by the equation:
\[
2x + 3y = 16.25
\]
2. Brett purchased 4 scones and 5 mugs of chai tea for \$[/tex]28.75. This gives us the equation:
[tex]\[
4x + 5y = 28.75
\][/tex]
Now, we have a system of two equations:
[tex]\[
\begin{align*}
2x + 3y &= 16.25 \\
4x + 5y &= 28.75
\end{align*}
\][/tex]
To solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we can use the method of elimination or substitution. Here, we'll outline the elimination method:
First, multiply the entire first equation by 2 to align coefficients for elimination:
[tex]\[
\begin{align*}
4x + 6y &= 32.50 \\
4x + 5y &= 28.75
\end{align*}
\][/tex]
Subtract the second equation from the modified first equation:
[tex]\[
(4x + 6y) - (4x + 5y) = 32.50 - 28.75
\][/tex]
Simplify:
[tex]\[
y = 3.75
\][/tex]
Now that we know [tex]\( y = 3.75 \)[/tex], substitute this value back into the first equation to solve for [tex]\( x \)[/tex]:
[tex]\[
2x + 3(3.75) = 16.25
\][/tex]
Calculate:
[tex]\[
2x + 11.25 = 16.25
\][/tex]
Subtract 11.25 from both sides:
[tex]\[
2x = 5.00
\][/tex]
Divide both sides by 2:
[tex]\[
x = 2.50
\][/tex]
Therefore, the cost of one scone is \[tex]$2.50, and the cost of one mug of chai tea is \$[/tex]3.75.
Let's define:
- [tex]\( x \)[/tex] as the cost of one scone.
- [tex]\( y \)[/tex] as the cost of one mug of chai tea.
From the problem, we can write the following equations based on the purchases:
1. Julianna purchased 2 scones and 3 mugs of chai tea for \[tex]$16.25. This can be represented by the equation:
\[
2x + 3y = 16.25
\]
2. Brett purchased 4 scones and 5 mugs of chai tea for \$[/tex]28.75. This gives us the equation:
[tex]\[
4x + 5y = 28.75
\][/tex]
Now, we have a system of two equations:
[tex]\[
\begin{align*}
2x + 3y &= 16.25 \\
4x + 5y &= 28.75
\end{align*}
\][/tex]
To solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we can use the method of elimination or substitution. Here, we'll outline the elimination method:
First, multiply the entire first equation by 2 to align coefficients for elimination:
[tex]\[
\begin{align*}
4x + 6y &= 32.50 \\
4x + 5y &= 28.75
\end{align*}
\][/tex]
Subtract the second equation from the modified first equation:
[tex]\[
(4x + 6y) - (4x + 5y) = 32.50 - 28.75
\][/tex]
Simplify:
[tex]\[
y = 3.75
\][/tex]
Now that we know [tex]\( y = 3.75 \)[/tex], substitute this value back into the first equation to solve for [tex]\( x \)[/tex]:
[tex]\[
2x + 3(3.75) = 16.25
\][/tex]
Calculate:
[tex]\[
2x + 11.25 = 16.25
\][/tex]
Subtract 11.25 from both sides:
[tex]\[
2x = 5.00
\][/tex]
Divide both sides by 2:
[tex]\[
x = 2.50
\][/tex]
Therefore, the cost of one scone is \[tex]$2.50, and the cost of one mug of chai tea is \$[/tex]3.75.
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