Question

Mr. Rose bought some small and large picture frames. He paid $3 for each small picture frame, and $5 for each large picture frame. He paid a total of $36 and bought a total of 10 frames. Write the two equations that could be used as a system to solve for the number of small frames, x, and large frames, y.

A) 3x + 5y = 36 and x + y = 10
B) 3x + 5y = 10 and x + y = 36
C) 5x + 3y = 36 and x + y = 10
D) 5x + 3y = 10 and x + y = 36

Answer 1

The correct system of equations for the number of small frames, x, and large frames, y, that Mr. Rose bought, is 3x + 5y = 36 for the total cost and x + y = 10 for the total number of frames.

Step-by-step explanation:

For Mr. Rose's purchase of picture frames, we need to find a system of equations that can be used to solve for the number of small frames, x, and large frames, y. He bought a total of 10 frames for $36, paying $3 for each small frame and $5 for each large frame. The two equations that represent this scenario are:

1. 3x + 5y = 36: This equation shows the total cost of buying x small frames and y large frames.
2. x + y = 10: This equation represents the total number of frames bought.

Using this system of equations, we can apply methods such as substitution or elimination to solve for x and y.