Question

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

Answer 1

Considering the definition of an equation, the number of students were surveyed is 96.

Definition of equation

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

An equation is made up of members, each of the expressions that appear on both sides of the equal sign, and terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

• When a value that is adding, when passing to the other member of the equation, it will subtract.
• If a value you are subtracting goes to the other side of the equation by adding.
• When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.
• If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.

Amount of students were surveyed

Being "x" the number of students were surveyed, and knowing that:

• 7 out of every 8 students surveyed own a bike. This means that if  8 students are surveyed, then 7 students own a bike.
• The difference between the number of students who own a bike and those who do not is 72.

you have:

• Number of students who own bike= 7/8x
• Number of students who do not own bike= 1/8x

The equation that represents this situation is:

7/8x - 1/8x= 72

Solving:

3/4x= 72

x= 72 ÷ 3/4

x= 96

Finally, the number of students were surveyed is 96.

Learn more about equations:

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