Question

Andy buys x cakes. Betty buys 4 times as many cakes as Andy. Colin buys 3 more cakes than Andy. Each cake costs 65p. The total cost of the cakes is £52.65. How many cakes did each person buy?

Answer 1

£ 13.00

your welcome

Answer 2

Each cake cost £ 13.00

Explanation:

We were given that, each cake costs
`65p` or £
`0.65`

Andy buys
`x` cakes.

Andy's cost is

£
`0.65x`

Betty buys 4 times as many cakes as Andy.

Betty's cost is

£
`0.65(4x)`

£
`2.60x`

Colin buys 3 more cakes than Andy

Colin's cost is

£
`0.65(x+3)`

The total cost of the cakes is £
`52.65`.

This implies that,

`0.65x+0.65(x+3)+2.60x=52.65`

We expand to get,

`0.65x+0.65x+1.95+2.60x=52.65`

We group like terms to get,

`0.65x+0.65x+2.60x=52.65-1.95`

This gives us,

`0.65x+0.65x+2.60x=52.65-1.95`

This implies that,

`3.9x=50.7`

`x=(50.7)/(3.9)`

`x=13`

Therefore each cake cost £ 13.00