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A bakery made 200 cakes in preparation for an upcoming holiday. Each cake was made from 4.5 cups of batter and 3.5 cups of frosting. Which of the following shows the number of cups of batter, b(f), the bakery used as a function of the f cups of frosting that the bakery used? Choose 1 answer: (A) b(f)=(7)/(9)f (B) b(f)=(200-7f)/(9) (c) b(f)=(9)/(7)f (D) b(f)=(200-9f)/(7)

A bakery made 200200 cakes in preparation for an upcoming holiday. Each cake was made from 44.55 cups of batter and 33.55 cups of frosting. Which of the following shows the number of cups of batter, b(f) b(f) , the bakery used as a function of the f f cups of frosting that the bakery used?\newlineChoose 11 answer:\newline(A) b(f)=79f b(f)=\frac{7}{9} f \newline(B) b(f)=200−7f9 b(f)=\frac{200-7 f}{9} \newline(C) b(f)=97f b(f)=\frac{9}{7} f \newline(D) b(f)=200−9f7 b(f)=\frac{200-9 f}{7}

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Q. A bakery made 200200 cakes in preparation for an upcoming holiday. Each cake was made from 44.55 cups of batter and 33.55 cups of frosting. Which of the following shows the number of cups of batter, b(f) b(f) , the bakery used as a function of the f f cups of frosting that the bakery used?\newlineChoose 11 answer:\newline(A) b(f)=79f b(f)=\frac{7}{9} f \newline(B) b(f)=200−7f9 b(f)=\frac{200-7 f}{9} \newline(C) b(f)=97f b(f)=\frac{9}{7} f \newline(D) b(f)=200−9f7 b(f)=\frac{200-9 f}{7}
  1. Given Information: We are given that each cake requires 4.54.5 cups of batter and 3.53.5 cups of frosting. To find the function b(f)b(f), we need to express the cups of batter in terms of the cups of frosting. Since the ratio of batter to frosting for each cake is constant, we can set up a proportion to find the relationship between batter and frosting.
  2. Proportion Setup: Let's denote the total number of cups of batter as BB and the total number of cups of frosting as FF. We know that for each cake, the ratio of batter to frosting is 4.53.5\frac{4.5}{3.5}. Since the bakery made 200200 cakes, we can write the following equations:\newlineB=4.5×200B = 4.5 \times 200\newlineF=3.5×200F = 3.5 \times 200
  3. Total Batter and Frosting: Now we calculate the total cups of batter and frosting used:\newlineB=4.5×200=900B = 4.5 \times 200 = 900 cups of batter\newlineF=3.5×200=700F = 3.5 \times 200 = 700 cups of frosting
  4. Ratio Calculation: We can now express the ratio of batter to frosting for all 200200 cakes. The ratio remains the same as for one cake, so we have:\newlineextbatter/extfrosting=4.5/3.5 ext{batter}/ ext{frosting} = 4.5/3.5\newlineLet's simplify this ratio:\newlineextbatter/extfrosting=(4.5/3.5)=(9/7) ext{batter}/ ext{frosting} = (4.5/3.5) = (9/7)
  5. Function Expression: We want to find b(f)b(f), the function that represents the number of cups of batter as a function of the number of cups of frosting. From the ratio we found, we can write:\newlineb(f)=97fb(f) = \frac{9}{7}f\newlineThis function tells us that for every 77 cups of frosting, we use 99 cups of batter.

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