Question

c) I have blots, bleets, and blits in a bag. The ratio of blots to bleets is 3:4. The ratio of bleets to blits is 5:6. What is the ratio of the number of blots to bits?

Answer 1

$\begin{gathered} \frac{\text{Number of blots}}{\text{Number of bleets}}\cdot\frac{\text{Number of bleets}}{\text{Number of blits}}=\frac{\text{Number of blots}}{\text{Number of blits}} \\ \frac{3}{4}\cdot\frac{5}{6}=\frac{15}{24} \end{gathered}$

Simplifying we have:

$\frac{15}{24}=\frac{3\cdot5}{3\cdot8}=\frac{5}{8}$

Then, the ratio of the number of blots to blits is 5:8.

b) ratio butter of sugar is 1:2. Then

$\frac{\text{butter}}{\text{sugar}}=\frac{1}{2}=\frac{x}{\frac{1}{2}\text{cup}}$

Solving the equation we have

$\begin{gathered} \frac{1}{2}=\frac{x}{\frac{1}{2}} \\ \frac{1}{2}\cdot\frac{1}{2}=x \\ \frac{1}{4}=x \end{gathered}$

Then, Jake needs 1/4 cup of butter.

Similarly, ratio flour of sugar is 1:2. Then

$\frac{\text{flour}}{\text{sugar}}=\frac{6}{2}=\frac{x}{\frac{1}{2}\text{cup}}$

Solving the equation we have

$\begin{gathered} \frac{6}{2}=\frac{x}{\frac{1}{2}} \\ \frac{6}{2}\cdot\frac{1}{2}=x \\ 3\cdot\frac{1}{2}=x \\ \frac{3}{2}=x \end{gathered}$

Then, Jake needs 3/2 cup of flour.

Finally, ratio sugar of milk is 2:1. Then

$\frac{\text{sugar}}{\text{milk}}=\frac{2}{1}=\frac{\frac{1}{2}\text{ cup}}{x}$

Solving the equation we have

$\begin{gathered} \frac{2}{1}=\frac{\frac{1}{2}}{x} \\ 2=\frac{\frac{1}{2}}{x} \\ 2x=\frac{1}{2} \\ x=\frac{\frac{1}{2}}{\frac{2}{1}} \\ x=\frac{1\cdot1}{2\cdot2} \\ x=\frac{1}{4} \end{gathered}$

Then, Jake needs 1/4 cup of milk.