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Darina [25.2K]
2 years ago
10

Anne, Barry, and Cathy enter a coffee shop. Anne orders two coffees, one juice, and two doughnuts and pays $7.50. Barry orders o

ne 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.
Mathematics
1 answer:
Evgesh-ka [11]2 years ago
7 0

Answer:

Coffee = $2.00

Juice = $1.50

Doughnut = $1.00

Step-by-step 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

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