Question

1. 14 books in 2 boxes; 20 books in 3 boxes

tell whether the two rates form a proportion.

1. \\(\frac{3.6}{m} = \frac{1.2}{3.6}\\)

solve the proportion.

1. \\(\frac{16}{10} = \frac{n + 2}{5}\\)
2. on monday, you swim 12 laps in 30 minutes. on tuesday, you swim 15 laps in 45 minutes. are these rates proportional? explain.

Explanation:

Problem 18:

Step1: Identify the rates

The two rates are $\frac{14}{2}$ (books per box) and $\frac{20}{3}$ (books per box).

Step2: Simplify the rates

Simplify $\frac{14}{2} = 7$ and $\frac{20}{3} \approx 6.67$.

Step3: Compare the rates

Since $7
eq 6.67$, the two rates do not form a proportion.

Step1: Cross - multiply the proportion

Given $\frac{3.6}{m}=\frac{1.2}{3.6}$, cross - multiply to get $1.2\times m = 3.6\times3.6$.

Step2: Calculate the right - hand side

$3.6\times3.6 = 12.96$. So the equation becomes $1.2m=12.96$.

Step3: Solve for m

Divide both sides of the equation by 1.2: $m=\frac{12.96}{1.2}=10.8$.

Step1: Cross - multiply the proportion

Given $\frac{16}{10}=\frac{n + 2}{5}$, cross - multiply to get $10\times(n + 2)=16\times5$.

Step2: Simplify both sides

$10n+20 = 80$.

Step3: Solve for n

Subtract 20 from both sides: $10n=80 - 20=60$. Then divide both sides by 10: $n = 6$.

Answer:

The two rates do not form a proportion.

Problem 19: