2-cycle

2-cycle engines require a mixture of oil to gas in order for them to run properly. For every gallon of gas, a certain 2-cycle engine requires 1 1/4 fl oz of oil. To prepare 3 1/2 gallon of gas, how much oil must be added to get the proper mixture?

Correct answer:

o₂ =  4 ³⁄₈ = 35/8 oz

Step-by-step explanation:

$$\begin{gathered} g_1=1\text{gal} \\ {o}_1=1\frac{1}{4}=1+\frac{1}{4}=\frac{1\cdot 4+1}{4}=\frac{4+1}{4}=\frac{5}{4}=1.25\text{oz} \\ {g}_2=3\frac{1}{2}=3+\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{6+1}{2}=\frac{7}{2}=3.5\text{gal} \\ {g}_1:o_1=g_2:o_2=const \\ {o}_1:g_1=o_2:g_2 \\ {o}_2=o_1\cdot \frac{g_2}{g_1}=\frac{5}{4}\cdot \frac{\frac{7}{2}}{1}=\frac{35}{8}\text{oz}=4\frac{3}{8}\text{oz}=4.375\text{oz} \end{gathered}$$

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