Question

A shop sells tins of paint in 2 litre and 5 litre cans. The manager checks the amount of paint he

has in stock, and finds that there are 500 cans altogether. These cans hold a total of 1420 litres of
paint. By forming and solving a pair of simultaneous equations, find the number of each size of
can in stock.

Answer 1

• 360 of 2 liter cans and 140 of 5 liter cans

Explanation:

Let the number of 2 liter cans be x and 5 liter cans be y.

Number of cans:

• x + y = 500

Amount of paint:

• 2x + 5y = 1420

Solve the system by elimination, double the first equation and subtract from the second one:

• 2x + 5y - 2x - 2y = 1420 - 2*500
• 3y = 420
• y = 420/3
• y = 140

Find x:

• x + 140 = 500
• x = 500 - 140
• x = 360