Miguel’s math tests are always out of 100 . The sum of the marks on his last three tests was 199 . His mark on the first math test was 60 . The product of his marks on the second and third tests was equal to 80 times his mark on the first test. Miguel wanted to create a system of equations that could help him determine his marks on his second and third tests.

Question

Miguel’s math tests are always out of 100 . The sum of the marks on his last three tests was 199 . His mark on the first math test was 60 . The product of his marks on the second and third tests was equal to 80 times his mark on the first test. Miguel wanted to create a system of equations that could help him determine his marks on his second and third tests.

If x represents Miguel’s mark on the second math test and y represents his mark on the third math test, which of the following systems of equations can be used to solve the given problem?

Answer 1

The problem states that "The product of his marks on the second and third tests was equal to 80 times his mark on the first test."

This can be represented by the equation:
xy = 80(60)

So, the first equation in the system is:
xy = 4800

The problem also states that "The sum of the marks on his last three tests was 199."

This can be represented by the equation:
x + y + 60 = 199

Simplifying this equation, we get:
x + y = 139

Therefore, the correct system of equations is:
xy = 4800
x + y = 139