Question

Answer numbers 1-4 with work please

Answer 1

Answer:

$\large\boxed{Q1.\ 6\dfrac{1}{4}\ cups}\\\boxed{Q2.\ 3\dfrac{1}{3}\ pounds}\\\boxed{Q3.\ 72:64=9:8}\\\boxed{Q4.\ 32:64=12:24}$

Step-by-step explanation:

In Q1 and Q2 we must make the proportion.

$Q1.\\s-\text{number of cups of sugar}\\\\\dfrac{2\frac{1}{2}}{\frac{2}{5}}=\dfrac{s}{1}\to s=2\dfrac{1}{2}:\dfrac{2}{5}=\dfrac{2\cdot2+1}{2}\cdot\dfrac{5}{2}=\dfrac{5}{2}\cdot\dfrac{5}{2}=\dfrac{25}{4}=6\dfrac{1}{4}$

$Q2.\\p-\text{number of pounds of mashed potatoes}\\\\\dfrac{2\frac{4}{6}}{\frac{4}{5}}=\dfrac{p}{1}\to p=2\dfrac{4}{6}:\dfrac{4}{5}=\dfrac{2\cdot6+4}{6}\cdot\dfrac{5}{4}=\dfrac{16\!\!\!\!\!\diagup^4}{6}\cdot\dfrac{5}{4\!\!\!\!\diagup_1}=\dfrac{20}{6}=\dfrac{20:2}{6:2}=\dfrac{10}{3}=3\dfrac{1}{3}$

$Q3.\\\\72:64=\dfrac{72}{64}=\dfrac{72:8}{64:8}=\dfrac{9}{8}=9:8\\\\\text{Other method}\\\\72:64=9:x\to\dfrac{72}{64}=\dfrac{9}{x}\qquad\text{cross multiply}\\\\72x=(64)(9)\qquad\text{divide both sides by 72}\\\\x=\dfrac{576}{72}\\\\x=8$

$Q4.\\\\32:x=12:24\\\\\dfrac{32}{x}=\dfrac{12}{24}\qquad\text{cross multiply}\\\\12x=(32)(24)\qquad\text{divide both sides by 12}\\\\x=\dfrac{768}{12}\\\\x=64$