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

Answer:

Each cake cost £ 13.00

Step-by-step 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,

$3.9x=50.7$

$x=\frac{50.7}{3.9}$

$x=13$

Therefore each cake cost £ 13.00