Question

Alexandra purchases two donuts and three cookies at the donut shop and it's charged $3.30. Brianna purchases five donuts and two cookies at the same shop for $4.95. All the donuts have the same price and all the cookies have the same price. What is the cost in dollars of each donut?

Answer 1

Given:

Cost of two donuts and three cookies = $3.30

Cost of five donuts and two cookies = $4.95

To find:

The cost of each donut.

Solution:

Let x be the cost of each donut and y be the cost of each cookie.

Cost of two donuts and three cookies = $3.30

`2x+3y=3.30` ...(i)

Cost of five donuts and two cookies = $4.95

`5x+2y=4.95` ...(ii)

Multiply equation (i) by 2.

`4x+6y=6.60` ...(iii)

Multiply equation (ii) by 3.

`15x+6y=14.85` ...(iv)

Subtracting (iii) from (iv), we get

`15x+6y-4x-6y=14.85-6.60`

`11x=8.25`

Divide both sides by 11.

`x=(8.25)/(11)`

`x=0.75`

Therefore, the cost of each donut is $0.75.