A sporting goods store sells footballs, basketballs, and volleyballs. A football costs $19, a baskeball costs $19, and a volleyball costs $7. On a given day, 2 times the number of footballs sold was the same as the number of volleyballs sold. The store brought in a total of $3750 that day, and the money made from basketballs alone was $66 more than the money made from volleyballs alone. Let x, y, z be the number of footballs, basketballs, and volleyballs sold respectively. Set up the matrix A that solves Ax = b, where x = and 3750 b = 66 A =
A sporting goods store sells footballs, basketballs, and volleyballs. A football costs $19, a baskeball costs $19, and a volleyball costs $7. On a given day, 2 times the number of footballs sold was the same as the number of volleyballs sold. The store brought in a total of $3750 that day, and the money made from basketballs alone was $66 more than the money made from volleyballs alone. Let x, y, z be the number of footballs, basketballs, and volleyballs sold respectively. Set up the matrix A that solves Ax = b, where x = and 3750 b = 66 A =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**HW11: Problem 1**
(1 point)
A sporting goods store sells footballs, basketballs, and volleyballs. A football costs $19, a basketball costs $19, and a volleyball costs $7. On a given day, 2 times the number of footballs sold was the same as the number of volleyballs sold. The store brought in a total of $3750 that day, and the money made from basketballs alone was $66 more than the money made from volleyballs alone. Let \( x, y, z \) be the number of footballs, basketballs, and volleyballs sold respectively. Set up the matrix \( A \) that solves \( Ax = b \), where
\[ x = \begin{bmatrix} x \\ y \\ z \end{bmatrix} \]
and
\[ b = \begin{bmatrix} 3750 \\ 0 \\ 66 \end{bmatrix} \]
\[ A = \begin{bmatrix} \, & \, & \, \\ \, & \, & \, \\ \, & \, & \, \end{bmatrix} \]
**Note:** You can earn partial credit on this problem.
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This problem involves setting up a system of equations to describe the sales scenario and solving it using matrix operations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc48e5dad-21e3-4575-8e1d-5a2bf1aa9af3%2F525954ef-4b0d-4393-a6d0-34284ca1d381%2Fxygdnz9_processed.png&w=3840&q=75)
Transcribed Image Text:**HW11: Problem 1**
(1 point)
A sporting goods store sells footballs, basketballs, and volleyballs. A football costs $19, a basketball costs $19, and a volleyball costs $7. On a given day, 2 times the number of footballs sold was the same as the number of volleyballs sold. The store brought in a total of $3750 that day, and the money made from basketballs alone was $66 more than the money made from volleyballs alone. Let \( x, y, z \) be the number of footballs, basketballs, and volleyballs sold respectively. Set up the matrix \( A \) that solves \( Ax = b \), where
\[ x = \begin{bmatrix} x \\ y \\ z \end{bmatrix} \]
and
\[ b = \begin{bmatrix} 3750 \\ 0 \\ 66 \end{bmatrix} \]
\[ A = \begin{bmatrix} \, & \, & \, \\ \, & \, & \, \\ \, & \, & \, \end{bmatrix} \]
**Note:** You can earn partial credit on this problem.
Buttons to:
- Preview My Answers
- Submit Answers
This problem involves setting up a system of equations to describe the sales scenario and solving it using matrix operations.
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