How to find c, j, and d?

Question

Anne: 2c + 2j + 2d = 8.00
Barry: 1c + 3d = 3.75
Cathy:3c + 1j + 4d = 9.25

 

( part of a world problem just stuck on how to solve the equations)

 

 

problem  is this: Anne, Barry, and Cathy carpool together and frequently stop to get breakfast for themselves at a cafe. Anne orders 2 coffees, 2 juice, 2 doughnuts and pays 8 dollars. Barry orders 1 coffee and 3 doughnuts and pays $3.75. Cathy orders three coffees, 1 juice, and 4 doughnuts and pays $9.25

Answer 1

steps:

 

1- start with the equation with the least number of variables, which in case would be Barry. create a relationship between c and d

c = 3.75 - 3d

 

2- the second step is to use the relationship between c and d and try to find a relationship between j and d. you can use equation 3 for that purpose

3c+j+4d=9.25

3(3.75-3d)+j+4d=9.25

11.25 - 9d + j + 4d = 9.25

j = 5d - 2

 

3- the third step is to use the two relationships between c and d and between j and d and use equation 1 to find the value of d

2c + 2j + 2d = 8

2 (3.75 - 3d) + 2 (5d - 2) + 2d = 8

7.5 - 6d + 10d - 4 + 2d = 8

6d = 4.5

d = $0.75 (the price of a donut is 75 cents)

 

4- the fourth and final step is to use the previously established relationships between c and d and between j and d and to find the value of c and j (i.e. the price of coffee and juice)

c = 3.75 - 3d = 3.75 - 3 x 0.75 = $1.50

j = 5d - 2 = 5 x 0.75 - 2 = $1.75

 

check

use equation 1 or 3 to make sure the numbers add up

2c + 2j + 2d = 8 (equation 1)

2 x 1.5 + 2 x 1.75 + 2 x 0.75 = 3 + 3.5 + 1.5 = 8 (OK)