Question

Which system of equations can be used to determine the number of days it will take for both to complete the same number of daily sit-ups?

A) Marisol: y = 32 + 2x, Kelly: y = 28 + 3x
B) Marisol: y = 28 + 2x, Kelly: y = 32 + 3x
C) Marisol: y = 32 + 3x, Kelly: y = 28 + 2x
D) Marisol: y = 28 + 3x, Kelly: y = 32 + 2x

Answer 1

The correct answer is option A, which includes a system of linear equations representing the number of sit-ups Marisol and Kelly do daily. By equating the two expressions and finding the value of x, we can determine the day when they do the same number of sit-ups.

Step-by-step explanation:

To determine the number of days it will take for Marisol and Kelly to complete the same number of daily sit-ups, we need to find the point at which their daily sit-up equations intersect. This is a problem of finding the solution to a system of linear equations. The equations represent the number of sit-ups (y) they can do after x days.

For example, if we take option A, Marisol's equation is y = 32 + 2x, and Kelly's equation is y = 28 + 3x. To find the day when they do the same number of sit-ups, we set the two equations equal to each other: 32 + 2x = 28 + 3x.

Calculation steps include isolating x:

1. Subtract 28 from both sides: 4 + 2x = 3x.
2. Subtract 2x from both sides: 4 = x.

Therefore, after 4 days, they will complete the same number of sit-ups.