Question

Paulo scored "x" on his first math test, then scored 10 points higher on his second, scored 5 points lower on the third than the second, and scored half as well on the fourth test as the second. if his average for the four tests is 75 points, what did he score on the second test?

Answer 1

We know that

`(x+(x+10)+(x+10-5)+ (x+10)/(2) )/(4) = 75`

Then we simplify to get this:

`((3x+15)+ (x+10)/(2) )/(4) = 75`

Then we get common denominators and add:

`( ((6x+30)/(2))+ ((x+10)/(2)) )/(4) = 75`

`( (7x+40)/(2) )/(4) = 75`

Then reciprocalize the main denominator and simplify:

`(7x+40)/(2) * (1)/(4) = 75`

`(7x+40)/(8) = 75`

And then solve for x:

`7x + 40 = 600`

`7x = 560`

`x = 80`

Since he scored ten points higher than x (x is what he earned in the first test), we can add:

`80 +10 = 90`

So, he got 90 points on his second test.