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Krunchy Kustard sells only two kinds of doughnuts: glazed an

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Krunchy Kustard sells only two kinds of doughnuts: glazed an [#permalink] New post 14 Jun 2018, 14:10
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Krunchy Kustard sells only two kinds of doughnuts: glazed and cream-filled. A glazed doughnut has 200 calories, and a cream-filled doughnut has 360 calories. If Felipe ate 5 doughnuts totaling 1,640 calories, how many were glazed?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[Reveal] Spoiler: OA

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Re: Krunchy Kustard sells only two kinds of doughnuts: glazed an [#permalink] New post 20 Jun 2018, 15:49
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sandy wrote:
Krunchy Kustard sells only two kinds of doughnuts: glazed and cream-filled. A glazed doughnut has 200 calories, and a cream-filled doughnut has 360 calories. If Felipe ate 5 doughnuts totaling 1,640 calories, how many were glazed?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


We can let g = the number of glazed filled donuts and c = the number of calories in cream filled donuts and create the equations:

g + c = 5

c = 5 - g

and

200g + 360c = 1640

20g + 36c = 164

5g + 9c = 41

Substituting (5 - g) for c, we have:

5g + 9(5 - g) = 41

5g + 45 - 9g = 41

4 = 4g

1 = g

Answer: A
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Re: Krunchy Kustard sells only two kinds of doughnuts: glazed an [#permalink] New post 05 Jul 2018, 01:41
Expert's post
Explanation

Assign variables to the two types of doughnuts, and write equations based on the given information:

Number of glazed = G

Number of cream-filled = C

\(G + C = 5\) (the number of doughnuts)
\(1,640 = 200 G + 360C\) (the number of calories)

The question asks for G, so isolate C in first equation and substitute into the second equation:

\(C = 5 - G\)

\(1,640 = 200G + 360(5 - G)\)

\(1,640 = 200G + 1,800 - 360G\)

\(1,640 = 1,800 - 160G\)

\(-160 = -160G\)

\(G = 1\)

Hence option A is correct!

Check the answer. If Felipe at 1 glazed doughnut, he ate 4 cream-filled doughnuts. He ate (1 × 200) + (4 × 360) = 200 + 1,440 = 1,640 calories.
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Re: Krunchy Kustard sells only two kinds of doughnuts: glazed an   [#permalink] 05 Jul 2018, 01:41
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