Question

lesson 5-5
use cross products to solve each proportion.

1. \\(\frac{8}{n} = \frac{12}{18}\\)
2. \\(\frac{4}{7} = \frac{p}{28}\\)
3. \\(\frac{u}{14} = -\frac{21}{28}\\)
4. \\(\frac{3}{21} = \frac{t}{49}\\)
5. \\(\frac{y}{35} = \frac{63}{45}\\)
6. \\(-\frac{6}{n} = -\frac{48}{12}\\)
7. \\(\frac{32}{x} = \frac{52}{117}\\)
8. \\(\frac{56}{80} = \frac{105}{m}\\)
9. the ratio of a persons weight on earth to his weight on the moon is 6 to 1. rafael weighs 90 pounds on earth. how much would he weigh on the moon?

Explanation:

Problem 21: $\boldsymbol{\frac{8}{n} = \frac{12}{18}}$

Step1: Apply cross - products

Cross - products of a proportion $\frac{a}{b}=\frac{c}{d}$ is $a\times d = b\times c$. So for $\frac{8}{n}=\frac{12}{18}$, we have $8\times18=n\times12$.
$\Rightarrow 144 = 12n$

Step2: Solve for $n$

Divide both sides of the equation by 12: $n=\frac{144}{12}=12$.

Step1: Apply cross - products

Using the cross - product rule $\frac{a}{b}=\frac{c}{d}\Rightarrow a\times d = b\times c$. For $\frac{4}{7}=\frac{p}{28}$, we get $4\times28 = 7\times p$.
$\Rightarrow 112=7p$

Step2: Solve for $p$

Divide both sides by 7: $p=\frac{112}{7} = 16$.

Step1: Apply cross - products

From $\frac{u}{14}=-\frac{21}{28}$, by cross - product rule, $u\times28=14\times(- 21)$.
$\Rightarrow 28u=-294$

Step2: Solve for $u$

Divide both sides by 28: $u=\frac{-294}{28}=-10.5$ or $u =-\frac{21}{2}$ (simplified fraction).

Answer:

$n = 12$

Problem 22: $\boldsymbol{\frac{4}{7}=\frac{p}{28}}$