SOLUTION: Seven out of every 8 students surveyed owns a bike. The difference between the number of students who own a bike and those who do not is 72. How many students were surveyed?

Question 1008840: Seven out of every 8 students surveyed owns a bike. The difference between the number of students who own a bike and those who do not is 72. How many students were surveyed?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x + y is the number of students who were surveyed.

x is the number who own a bike.
y is the number who don't.

the ratio of the ones who own a bike and the ones who were surveyed is x / (x + y)

that ratio is 7/8.

you get x / (x + y) = 7/8

multiply both sides of this equation by (x + y) to get x = (x + y) * 7/8

simplify to get x = 7/8 * x + 7/8 * y

subtract 7/8 * x from both sides of this equation to get:

1/8 * x = 7/8 * y

solve for x to get x = 7 * y

this means that the number of students who own a bike is 7 times the number of students who don't.

divide both sides of that equation by y to get x/y = 7/1.

that means that the ratio of students who own a bike to the number of students who don't is equal to 7/1.

the problem states that the difference between the number who own a bike and the number who don't is 72.

this means that x - y = 72

from the equation of x = 7 * y, replace x with 7 * y in the equation of x - y = 72 to get:

7 * y - y = 72

simplify to get 6 * y = 72

divide both sides of that equation by 6 to get y = 72/6 = 12

this means that the number of students who do not own a bike is 12.

since x = 7 * y, then x = 7 * 12 = 84.

this means that the number of students who own a bike is 84.

since the number of students is x + y, this means that the number of students who were surveyed is 84 + 12 = 96.

let's see if this is right.

96 students were surveyed.

84 own a bike and 12 don't.

the difference between the ones who own a bike and the ones who don't is 84 - 12 = 72.

the ratio of the ones who own a bike and the number surveyed is 84/96 = 7/8.

numbers look good.

solution is 96 students were surveyed.
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