Answer:
Each cake cost £ 13.00
Step-by-step explanation:
We were given that, each cake costs [tex]65p[/tex] or £ [tex]0.65[/tex]
Andy buys [tex]x[/tex] cakes.
Andy's cost is
£[tex]0.65x[/tex]
Betty buys 4 times as many cakes as Andy.
Betty's cost is
£[tex]0.65(4x)[/tex]
£[tex]2.60x[/tex]
Colin buys 3 more cakes than Andy
Colin's cost is
£[tex]0.65(x+3)[/tex]
The total cost of the cakes is £ [tex]52.65[/tex].
This implies that,
[tex]0.65x+0.65(x+3)+2.60x=52.65[/tex]
We expand to get,
[tex]0.65x+0.65x+1.95+2.60x=52.65[/tex]
We group like terms to get,
[tex]0.65x+0.65x+2.60x=52.65-1.95[/tex]
This gives us,
[tex]0.65x+0.65x+2.60x=52.65-1.95[/tex]
This implies that,
[tex]3.9x=50.7[/tex]
[tex]x=\frac{50.7}{3.9}[/tex]
[tex]x=13[/tex]
Therefore each cake cost £ 13.00
