Question

1. On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at thecost of $16.50. It turns out that the doughnuts were more popular than thecoffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of$14.25. How much was each cup of coffee and each doughnut? The coffeecost $1.25 and a doughnut is $0.80.

Answer 1

A coffee costs $1.25 and a doughnut is $0.80.

Step-by-step explanation

Let the price of each doughnut be x;

Let the price of each coffee be y

If Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50, then;

5x + 10y = 16.50 .... 1

Also, if he bought 5 cups of coffee and 10 doughnuts for a total of $14.25, then;

10x + 5y = 14.25 .... 2

Solve both equations simultaneously

Multiply equation 1 by 2 and subtract from equation 2

Equation 1 * 2:

2(5x) + 2(10y) = 2(16.50)

10x + 20y = 33 ..... 3

Subtract 2 from 3

(10x-10x) +(5y - 20y) = 14.25 - 33

-15y = -18.75

y = -18.75/15

y = 1.25

Substitute y = 1.25 into equation 1

From 2: 10x + 5y = 14.25

10x + 5(1.25) = 14.25

10x + 6.25 = 14.25

10x = 14.25 - 6.25

10x = 8

x = 8/10

x = 0.8

Hence a coffee costs $1.25 and a doughnut is $0.80.