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A cake manufacturer boxes Swiss chocolate and German chocolate cakes at one site. A box of Swiss chocolate cake contains 0.55 lb of a sugar mixture and 0.45 lb of flour. A box of German chocolate cake contains 0.59 lb of the sugar mixture and 0.41 lb of flour. Each day at this site, the company has available 2,300 lb of the sugar mixture and 1,700 lb of flour. If all the ingrediates are utilized how many boxes of each type of cake can be made each day?

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Answer:

2,500 German chocolate cake boxes.

1,500 Swiss chocolate cake boxes.

Step-by-step explanation:

Let 'S' be the number of Swiss chocolate cakes boxed and 'G' the number of German cholocate cakes boxed. If all of the available ingredients are used:

[tex]0.55*S +0.59*G = 2,300\\0.45*S+0.41*G = 1,700[/tex]

Solving the linear system above:

[tex](0.55 *S +0.59*G)- \frac{0.55}{0.45} (0.45*S+0.41*G)= 2,300-\frac{0.55}{0.45}*1,700*\\0.088888*G = 222.222\\G=2,500\\S =\frac{2,300-2,500*0.59}{0.55}\\S=1500[/tex]

2,500 German chocolate cake boxes and 1,500 Swiss chocolate cake boxes can be made each day.

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