Question

Ahmed sells different types of cake in his shop.

The cost of each cake depends on its type and its size.
Every small cake costs $x and every large cake costs $(2x + 1).

The number of small cherry cakes that can be bought for $4 is the same as the number of large
cherry cakes that can be bought for $13.
Find the cost of a small cherry cake.

Answer 1

$0.80

Explanation:

Let y be the number of cakes that can be bought then...

xy=4

y(2x+1)=13

Distribute the y to each term in the parentheses...

y(2x)+y(1)=13

2xy+y=13

xy=4

Multiply the second equation by 2...

2xy+y=13

2xy=8

Solve the equation using elimination (subtract the two equations and eliminate 2xy)...

y=13-8=5

Now, plug 5 back in for y to solve for x...

xy=4

5x=4

Divide both sides by 5

x=$0.80