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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.

Sagot :

MrRoyal

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]

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