Solving linear equations

Question

one hundred and ninety students go on a tour. They go on minibuses that carry 14passengers each and In buses that carry 40 passengers each. There were eight vehicles used in full. How many of each type of vehicle were used?

Answer 1

Let's start with

x = number of minibuses

y = number of buses

 

x + y = 8 (1)

14x + 40y = 190 (2)

 

We can factor out 2 from our second equation, it gives us

7x + 20y = 95

 

We can use substitution

x = 8 - y

 

Put in our value of x into our equation

7(8 - y) + 20y = 95

56 - 7y + 20y = 95

13y = 39

y = 3

 

Use our value of y into the first equation

x + 3 = 8

x = 5

 

Check your answer by using the original equation

14(5) + 40(3) = 190

70 + 120 = 190

190 = 190

 

So there are 5 minibuses and 3 buses.