Answer:
Coffee = $2.00
Juice = $1.50
Doughnut = $1.00
Step-by-step explanation:
Given
Let:
[tex]c = coffee\\ j= juice\\ d = doughnut[/tex]
So, we have:
Anna
[tex]2c + j + 2d = 7.50[/tex]
Barry
[tex]c + 3d = 5.00[/tex]
Cathy
[tex]3c + j + 4d = 11.50[/tex]
Required
The price of each
We have:
[tex]2c + j + 2d = 7.50[/tex]
[tex]c + 3d = 5.00[/tex]
[tex]3c + j + 4d = 11.50[/tex]
Make c the subject in: [tex]c + 3d = 5.00[/tex]
[tex]c = 5.00 - 3d[/tex]
Substitute [tex]c = 5.00 - 3d[/tex] in [tex]2c + j + 2d = 7.50[/tex] and [tex]3c + j + 4d = 11.50[/tex]
[tex]2c + j + 2d = 7.50[/tex]
[tex]2[5.00 - 3d] + j + 2d = 7.50[/tex]
[tex]10.00 - 6d+ j + 2d = 7.50[/tex]
Make j the subject
[tex]j = 7.50 - 10.0 +6d - 2d[/tex]
[tex]j = -2.50 +4d[/tex]
[tex]3c + j + 4d = 11.50[/tex]
[tex]3[5.00 - 3d] + j + 4d = 11.50[/tex]
[tex]15.00 - 9d + j + 4d = 11.50[/tex]
Make j the subject
[tex]j = 11.50 - 15.00 + 9d -4d[/tex]
[tex]j = -3.50 + 5d[/tex]
So, we have:
[tex]j = -3.50 + 5d[/tex] and [tex]j = -2.50 +4d[/tex]
Equate both values of j
[tex]-3.50 + 5d = -2.50 + 4d[/tex]
Collect like terms
[tex]5d - 4d = 3.50 -2.50[/tex]
[tex]d = 1.00[/tex]
Substitute [tex]d = 1.00[/tex] in [tex]j = -3.50 + 5d[/tex]
[tex]j = -3.50 + 5d[/tex]
[tex]j = -3.50 + 5 * 1.00[/tex]
[tex]j = -3.50 + 5.00[/tex]
[tex]j = 1.50[/tex]
To solve for c, we substitute [tex]d = 1.00[/tex] in [tex]c + 3d = 5.00[/tex]
[tex]c + 3 * 1.00 =5.00[/tex]
[tex]c + 3.00 =5.00[/tex]
Solve for c
[tex]c =- 3.00 +5.00[/tex]
[tex]c =2.00[/tex]
