Question 1008840
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.