write an equation to model the situation. then solve the equation. 28. one company charges a flat fee of…

Explanation:

Step1: Set up the cost - equations

Let $h$ be the number of hours. The cost $C_1$ for the first company is $C_1 = 250+20h$. The cost $C_2$ for the second company is $C_2=400 + 12h$. Set $C_1 = C_2$: $250+20h=400 + 12h$.

Step2: Isolate the variable terms

Subtract $12h$ from both sides: $250+20h-12h=400 + 12h-12h$, which simplifies to $250 + 8h=400$.

Step3: Isolate the constant terms

Subtract 250 from both sides: $250-250 + 8h=400-250$, resulting in $8h=150$.

Step4: Solve for $h$

Divide both sides by 8: $h=\frac{150}{8}=\frac{75}{4}=18.75$.

Answer:

$18.75$ hours

Explanation for 29:

Step1: Cross - multiply

For the proportion $\frac{4}{2}=\frac{5}{a}$, cross - multiplying gives $4a=2\times5$.

Step2: Solve for $a$

$4a = 10$, so $a=\frac{10}{4}=\frac{5}{2}$. There are no restricted values since the denominator of the original non - variable fraction is non - zero and the variable $a$ is in the denominator of a single fraction and $a = 0$ is not a solution.

Answer for 29:

$a=\frac{5}{2}$

Explanation for 30:

Step1: Cross - multiply

For the proportion $\frac{3}{8n}=\frac{4}{5}$, cross - multiplying gives $3\times5=4\times8n$.

Step2: Simplify and solve for $n$

$15 = 32n$, so $n=\frac{15}{32}$. The restricted value is $n = 0$ because if $n = 0$, the left - hand side $\frac{3}{8n}$ is undefined.

Answer for 30:

$n=\frac{15}{32}$, restricted value $n = 0$

Explanation for 31:

Step1: Cross - multiply

For the proportion $\frac{4}{3}=\frac{6}{r - 5}$, cross - multiplying gives $4(r - 5)=3\times6$.

Step2: Expand and solve for $r$

$4r-20 = 18$. Add 20 to both sides: $4r=18 + 20=38$. Then $r=\frac{38}{4}=\frac{19}{2}$. The restricted value is $r = 5$ because if $r = 5$, the right - hand side $\frac{6}{r - 5}$ is undefined.

Answer for 31:

$r=\frac{19}{2}$, restricted value $r = 5$

Explanation for 32:

Step1: Cross - multiply

For the proportion $\frac{x}{9}=\frac{x - 7}{10}$, cross - multiplying gives $10x=9(x - 7)$.

Step2: Expand and solve for $x$

$10x=9x-63$. Subtract $9x$ from both sides: $10x-9x=9x-9x - 63$, so $x=-63$. There are no restricted values since the denominators 9 and 10 are non - zero.

Answer for 32:

$x=-63$