Question

question 28 points 2

heather bought two sizes of ceramic tiles. each size was a different price. the matrix equation \\(\

$$\begin{bmatrix} 1 & 1 \\\\ 1 & 2 \\end{bmatrix}$$

\

$$\begin{bmatrix} x \\\\ y \\end{bmatrix}$$

= \

$$\begin{bmatrix} 50 \\\\ 80 \\end{bmatrix}$$

\\) can be used to solve the number of small tiles (x) and large tiles (y). how many small tiles did she buy?

25

20

Explanation:

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<reasoning>

Set up the system of equations

Using the Solving Matrix Equations knowledge point
\[

$$\begin{aligned} 1x + 1y &= 50 \\ 1x + 2y &= 80 \end{aligned}$$

\]

Solve for the variables

Subtract the first equation from the second equation to eliminate \(x\):
\[
(1x + 2y) - (1x + 1y) = 80 - 50
\]
\[
y = 30
\]

Substitute \(y = 30\) back into the first equation to find \(x\):
\[
x + 30 = 50
\]
\[
x = 20
\]

Identify the target value

The variable \(x\) represents the number of small tiles.
\[
x = 20
\]
</reasoning>

<answer>
<mcq-option>25</mcq-option>
<mcq-correct>20</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
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Answer:

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<reasoning>

Set up the system of equations

Using the Solving Matrix Equations knowledge point
\[

$$\begin{aligned} 1x + 1y &= 50 \\ 1x + 2y &= 80 \end{aligned}$$

\]

Solve for the variables

Subtract the first equation from the second equation to eliminate \(x\):
\[
(1x + 2y) - (1x + 1y) = 80 - 50
\]
\[
y = 30
\]

Substitute \(y = 30\) back into the first equation to find \(x\):
\[
x + 30 = 50
\]
\[
x = 20
\]

Identify the target value

The variable \(x\) represents the number of small tiles.
\[
x = 20
\]
</reasoning>

<answer>
<mcq-option>25</mcq-option>
<mcq-correct>20</mcq-correct>
</answer>

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