Systems of Linear Equations (Word Problem)

[deelitefulady]

I need help solving this equation. Systems of Linear Equations - Applications

A manufacturer produces two models of the same toy, Model A and Model B. Model A takes 4 hours to produce and costs $8 each. Model B takes 3 hours to produce and costs $7 each. If the manufacturer allots a total of 5800 hours and $12,600 for production each week, how many of each model will be produced?

I cannot figure out how to set this problem up. This is from Intermediate Algebra 5th Edition (Author: Wright) Chapter 3.2 Problem 30.

thank you

 

[Loren]

I think it would be helpful to figure out what happens in one hour.

 

[soroban]

Hello, deelitefulady!

A manufacturer produces two models of the same toy, Model A and Model B.
Model A takes 4 hours to produce and costs $8 each.
Model B takes 3 hours to produce and costs $7 each.
If the manufacturer allots a total of 5800 hours and $12,600 for production each week,
how many of each model will be produced?

\(\displaystyle \text{Let }x\text{ = number of A's made weekly.}\)
\(\displaystyle \text{Let }y\text{ = number of B's made weekly.}\)

\(\displaystyle \text{We have: }\;\begin{array}{|c||c|c|}\hline & \text{Time} & \text{Cost} \\ \hline\hline A\x) & 4x & 8x \\\hline B\y) & 3y & 7y \\ \hline \hline \text{Total} & 5,800 & 12,600 \\ \hline \end{array}\)


\(\displaystyle \text{Read down the columns: }\;\begin{Bmatrix} 4x + 3y &=&5,800 \\ 8x + 7y &=& 12,600 \end{Bmatrix}\)