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Answer:
x/y = 5/9
Step-by-step 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