Question

The cost of 2 footballs and 3 tennis balls is £21.73.

The cost of 5 footballs and 7 tennis balls is £53.20.
Work out the cost of
a) a football.
b) a tennis ball.

Answer 1

Answer: A) £7.49

B) £2.25

Explanation:

Step 1:

Let the cost of a football be
`f`and the cost of a tennis ball be
`t`.

Step 2:

Write the 2 equations we have from the given information:

`2f + 3t = 21.73`
`\textsf{(from the cost of 2 footballs and 3 tennis balls)}`

`5f + 7t = 53.20`
`\textsf{(from the cost of 5 footballs and 7 tennis balls)}`

Step 3:

Solve for one variable in one of the equations. For example, we can solve for
`f`in the first equation:

• 
  `2f + 3t = 21.73`
• 
  `2f = 21.73 - 3t`
• 
  `f = ((21.73 - 3t))/(2)`

Step 4:

Substitute this expression for
`f` into the second equation and solve for
`t`:

• 
  `5f + 7t = 53.20`
• 
  `5[((21.73 - 3t))/(2)] + 7t = 53.20`
• 
  `54.325 - 7.5t + 7t = 53.20`
• 
  `0.5t = 1.125`
• 
  `t = 2.25`

So, the cost of a tennis ball is £2.25.

Step 5:

Substitute this value of
`t` into the expression for
`f` and solve for
`f`:

• 
  `f = ((21.73 - 3t))/(2)`

• 
  `f = ((21.73 - 3(2.25)))/(2)`

• 
  `f = 7.49`

So, the cost of a football is £7.49

Step 6:

Therefore, the cost of a football is £7.49 and the cost of a tennis ball is £2.25.