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On the first day of a two-day meeting, 10 coffees and 10 doughnuts were purchased for a total of $20.00. Since nobody drank the coffee and all the doughnuts were eaten, the next day only 2 coffees and 14 doughnuts were purchased for a total of $13.00. How much did each coffee and each doughnut cost?

Respuesta :

Answer:

1.25 dollars- the value of each coffee

0.75 dollars- the value of each doughnut

Step-by-step explanation:

Suppose that value of one coffee is x dollars, when one doughnut costs y dollars. The value o 10 coffee is 10x, when 10 doughnuts cost 10y. The sum is 10x+10y and it is 20.

10x+10y= 20 (we can divide each part by 10)

x+y=2

2coffee cost  2x, 14 doughnuts cost 14y

2x+14y=13 (it can be divided by two)

x+7y=6.5

We have the system of equations x+y=2,  x+7y=6.5

Subtract the first equation from the second one (the left side of the first equation from the left side

x+7y - (x+y)= 6.5-2

6y=4.5

y=4.5/6= 3/4 = 0.75 dollars- the value of each doughnut

x=2-0.75=1.25 dollars- the value of each coffee

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