Question

A ride at a carnival has two types of cars for children to ride one type has two seats and one has four seats there are 25 cars and they can seat a total of 70 children how many four seated cars are there

Answer 1

10

Explanation:

To solve this problem you need to create a system of equations. In these equations, use a = 2-seated car and b = 4- seated car

The first equation that you can make can be a + b = 25 because the number of 2-seated cars plus the number of 4-seated cars is going to equal a total of 25 cars.

The next equation you can make is 2a + 4b = 70 because the number of seats provided by the 2-seated cars plus the number of seats provided by the 4-seated cars will equal 70 total seats.

Next, line up the equations and solve:

Step one: Line up the equations

a + b = 25

2a + 4b = 70

Step two: Multiply the top equation by -2 so that you can add both of the equations together

-2(a) + -2(b) = 25(-2) ⇒ -2a - 2b = -50

2a + 4b = 70 ⇒ 2a + 4b = 70

Step three: Add the equations

-2a - 2b = -50

+ 2a + 4b = 70

______________

2b = 20

Step four: Divide both sides by 2 in order to solve for b

2b = 20 ⇒ b = 10

Because b represents the number of 4-seated cars, you now know that there are 10 4-seated cars on the ride.