Henry has a mix of vans and cars. When he loads 2 vans and 3 cars, he can fit a total of 21 people. When he loads 4 vans and 1 car, he can fit 27 people.

Question

I need help on how to turn it into an equation

 

Answer 1

HI, Kareena!

Okay, so I'm assuming you need to find out how many people fit in a car and how many fit in a van.

 

Ok, let's let:

X = number of people in a van

Y = number of people in a car

 

The, we have 2 equations and 2 variables:

2X + 3Y = 21

4X + 1Y = 27

 

Now, you can multiply the first equation by 2 and then subtract the equations:

 

2(2X + 3Y = 21) =

4X + 6Y = 42

 

4X + 6Y = 42

4X + 1Y = 27

----------------

subtract the equations:

5Y = 15

Y = 3

then solve for X:

2X + 9 = 21

2X = 12

X = 6

Therefore:

6 people can fit in a van

3 people can fit in a car

 

 

 

Answer 2

Number of vans = v

number of cars = c

 

2v +3c =21

4v + 1c = 27