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.

$x=\dfrac{8.25}{11}$

$x=0.75$

Therefore, the cost of each donut is $0.75.