Question

Anne, Barry, and Cathy enter a coffee shop. Anne orders two coffees, one juice, and two doughnuts and pays $7.50. Barry orders one coffee and three doughnuts and pays $5.00. Cathy orders three coffees, one juice, and four doughnuts and pays $11.50. Find the price of coffee, juice, and doughnuts at this coffee shop.

Answer 1

Coffee = $2.00

Juice = $1.50

Doughnut = $1.00

Explanation:

Given

Let:

`c = coffee\\ j= juice\\ d = doughnut`

So, we have:

Anna

`2c + j + 2d = 7.50`

Barry

`c + 3d = 5.00`

Cathy

`3c + j + 4d = 11.50`

Required

The price of each

We have:

`2c + j + 2d = 7.50`

`c + 3d = 5.00`

`3c + j + 4d = 11.50`

Make c the subject in:
`c + 3d = 5.00`

`c = 5.00 - 3d`

Substitute
`c = 5.00 - 3d` in
`2c + j + 2d = 7.50` and
`3c + j + 4d = 11.50`

`2c + j + 2d = 7.50`

`2[5.00 - 3d] + j + 2d = 7.50`

`10.00 - 6d+ j + 2d = 7.50`

Make j the subject

`j = 7.50 - 10.0 +6d - 2d`

`j = -2.50 +4d`

`3c + j + 4d = 11.50`

`3[5.00 - 3d] + j + 4d = 11.50`

`15.00 - 9d + j + 4d = 11.50`

Make j the subject

`j = 11.50 - 15.00 + 9d -4d`

`j = -3.50 + 5d`

So, we have:

`j = -3.50 + 5d` and
`j = -2.50 +4d`

Equate both values of j

`-3.50 + 5d = -2.50 + 4d`

Collect like terms

`5d - 4d = 3.50 -2.50`

`d = 1.00`

Substitute
`d = 1.00` in
`j = -3.50 + 5d`

`j = -3.50 + 5d`

`j = -3.50 + 5 * 1.00`

`j = -3.50 + 5.00`

`j = 1.50`

To solve for c, we substitute
`d = 1.00` in
`c + 3d = 5.00`

`c + 3 * 1.00 =5.00`

`c + 3.00 =5.00`

Solve for c

`c =- 3.00 +5.00`

`c =2.00`