Answer:
[tex]\textsf{c) \quad $1 \frac{1}{2}$ cups of broccoli per 1 lb of beef}.[/tex]
Step-by-step explanation:
Given information:
- For every ³/₄ lb of beef, the recipe calls for ⁹/₈ cups of broccoli.
Create a ratio of pounds of beef to cups of broccoli, where x is the number of cups of broccoli to one pound of beef:
[tex]\implies \dfrac{3}{4}: \dfrac{9}{8}=1:x[/tex]
[tex]\implies \dfrac{\frac{3}{4}}{\frac{9}{8}}=\dfrac{1}{x}[/tex]
Cross multiply:
[tex]\implies \dfrac{3}{4}x=\dfrac{9}{8}[/tex]
[tex]\implies x=\dfrac{9}{8} \div \dfrac{3}{4}[/tex]
To divide fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:
[tex]\implies x=\dfrac{9}{8} \times \dfrac{4}{3}[/tex]
[tex]\implies x=\dfrac{9 \times 4}{8 \times 3}[/tex]
[tex]\implies x=\dfrac{36}{24}[/tex]
[tex]\implies x=\dfrac{3 \cdot \diagup\!\!\!\!\!\!12}{2 \cdot \diagup\!\!\!\!\!\!12}[/tex]
[tex]\implies x=\dfrac{3}{2}[/tex]
[tex]\implies x=1 \frac{1}{2}[/tex]
Therefore, 1¹/₂ cups of broccoli would be needed to one pound of beef.
