Omar stopped at a donut shop every day on his way to work. Last week he had eight donuts and five cappuccinos which gave him a total of 3000 calories. This week he had six donuts and three cappuccinos which was a total of 2160 cal. How many calories are in one doughnut? How many calories are in one cappuccino?

Donuts=d. Cappuccino =c
8d+6c=3000
6d+3c=2160
Multiply second equation by 2
12d+6c=4320
Subtract
8d+6c=3000
12d+6c=4320
-4d=-1320
d=330
Plug back into original equation
6d+3c=2160
6(330)+3c=2160
1980+3c=2160
c=60
Donuts 330 calories
Cappuccino 60 calories

Answer Link

boffeemadrid boffeemadrid · Answer 2 · 2021-10-28T14:02:54+02:00

The calories in one doughnut and one cappuccino is required.

The calories in one doughnut is 300 and one cappuccino is 120.

Let x be the calories in one doughnut

y be the calories in one cappuccino

The equations will be

[tex]8x+5y=3000[/tex] [tex]\times3[/tex]

[tex]6x+3y=2160[/tex] [tex]\times5[/tex]

[tex]24x+15y=9000[/tex]

[tex]30x+15y=10800[/tex]

Subtracting the equations

[tex]-6x=-1800\\\Rightarrow x=\dfrac{1800}{6}\\\Rightarrow x=300[/tex]

For y

[tex]8x+5y=3000\\\Rightarrow y=\dfrac{3000-8x}{5}=\dfrac{3000-8\times 300}{5}\\\Rightarrow y=120[/tex]

The calories in one doughnut is 300 and one cappuccino is 120.

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