A baker 6

A baker prepares a cake mix that weighs 120 pounds. The cake mix consists of 25 1/2 pounds of flour, 32 3/4 pounds of sugar, 20 3/8 pounds of milk, 15 pounds of whole eggs, and a total of 7 1/4 pounds of miscellaneous ingredients. The only other ingredient is shortening. How many pounds of shortening are used in the mix?

Final Answer:

x =  19 ¹⁄₈ = 153/8 lb

Step-by-step explanation:

$$\begin{gathered} a=120\text{lb} \\ b=25\frac{1}{2}=\frac{51}{2}=25.5\text{lb} \\ c=32\frac{3}{4}=\frac{131}{4}=32.75\text{lb} \\ d=20\frac{3}{8}=20+\frac{3}{8}=\frac{20\cdot 8+3}{8}=\frac{160+3}{8}=\frac{163}{8}=20.375\text{lb} \\ e=15\text{lb} \\ f=7\frac{1}{4}=7+\frac{1}{4}=\frac{7\cdot 4+1}{4}=\frac{28+1}{4}=\frac{29}{4}=7.25\text{lb} \\ g=b+c+d+e+f=\frac{51}{2}+\frac{131}{4}+\frac{163}{8}+15+\frac{29}{4}=\frac{807}{8}=100.875\text{lb} \\ x=a-g=120-\frac{807}{8}=\frac{120\cdot 8}{8}-\frac{807}{8}=\frac{960}{8}-\frac{807}{8}=\frac{960-807}{8}=\frac{153}{8}=\frac{153}{8}\text{lb}=19\frac{1}{8}\text{lb}=19.125\text{lb} \end{gathered}$$

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