Question

Michael, Jacob, and Donald are comparing how many points they each received in math over the course of the nine weeks. Michael gained 10 less than twice as many points as Jacob. Donald earned half as many as Michael. Together, they had a combined total of 1,245 points. How many points did each of them have?

Answer 1

Michael = 620 Points

Jacob = 315 Points

Donald = 310 Points

Explanation:

Let points of Michael be m, Jacob be j, and Donald be d.

Let's write some equations from the information given.

m = 2j - 10

d = 0.5m

m + j + d = 1245

Let's put 1st equation into 2:

d = 0.5m

d = 0.5(2j - 10)

d = j - 5

Now replace 3rd equation with this and first:

m + j + d = 1245

2j - 10 + j + j - 5 = 1245

4j - 15 = 1245

4j = 1260

j = 1260/4 = 315

Now, we know d = j - 5, so

d = 315 - 5

d = 310

and we also know m = 2j - 10, so

m = 2(315) - 10 = 630 - 10 = 620

Michael = 620 Points

Jacob = 315 Points

Donald = 310 Points