Question

The average of the test scores of a

group of x students is 76 and the average of the test scores of a group of y students is 90. When the scores of the two groups of students are combined, the average test score is 85. What is the value of x/y

Answer 1

x/y = 5/9

Explanation:

sum = count * mean

for the group of x students:

sum = x * 76

let's say this sum is a

a = 76x

for the group of y students:

sum = y * 90

let's say this sum is b

b = 90y

total sum = total count * total mean

total sum = total sum from both groups = a + b

total count = total count from both groups = x + y

a + b = (x+y) * 85

expand

a + b = 85x + 85y

a = 76x

b = 90y

replace a with 76x and b with 90y in the first equation. this limits the equation to x and y, which we want because we want to find x/y

76x + 90y = 85x + 85y

subtract 76x and 85y from both sides to limit the amount of numbers

5y = 9x

divide both sides by 9 to isolate the x

(5/9)y = x

divide both sides by y to get x/y

x/y = 5/9