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
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Sandy
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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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Sandy
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