Question

question 1 (2 points) solve each proportion. your answer may be a decimal. round to the nearest tenth. 1. \\(\frac{9}{16} = \frac{x}{12}\\) \\(x = \underline{\quad\quad}\\) 2. \\(\frac{7}{11} = \frac{18}{x + 1}\\) \\(x = \underline{\quad\quad}\\) 3. \\(\frac{17}{15} = \frac{10}{2x - 2}\\) \\(x = \underline{\quad\quad}\\) 4. \\(\frac{6}{19} = \frac{x - 12}{2x - 2}\\) \\(x = \underline{\quad\quad}\\) blank 1: \\(\underline{\quad\quad}\\) blank 2: \\(\underline{\quad\quad}\\) blank 3: \\(\underline{\quad\quad}\\) blank 4: \\(\underline{\quad\quad}\\)

Explanation:

Problem 1: $\boldsymbol{\frac{9}{16} = \frac{x}{12}}$

Step1: Cross - multiply

We know that for a proportion $\frac{a}{b}=\frac{c}{d}$, we have $a\times d = b\times c$. So for $\frac{9}{16}=\frac{x}{12}$, we get $9\times12 = 16\times x$.
$108 = 16x$

Step2: Solve for $x$

Divide both sides of the equation by 16: $x=\frac{108}{16}=6.75$. Rounding to the nearest tenth, $x = 6.8$ (since the hundredth digit is 5, we round up the tenth digit).

Step1: Cross - multiply

Using the cross - multiplication rule for proportions $\frac{a}{b}=\frac{c}{d}\Rightarrow a\times d=b\times c$, we have $7\times(x + 1)=11\times18$.
$7x+7 = 198$

Step2: Isolate the variable term

Subtract 7 from both sides: $7x=198 - 7=191$.

Step3: Solve for $x$

Divide both sides by 7: $x=\frac{191}{7}\approx27.3$ (rounded to the nearest tenth).

Step1: Cross - multiply

Applying cross - multiplication: $17\times(2x - 2)=15\times10$.
$34x-34 = 150$

Step2: Isolate the variable term

Add 34 to both sides: $34x=150 + 34=184$.

Step3: Solve for $x$

Divide both sides by 34: $x=\frac{184}{34}\approx5.4$ (rounded to the nearest tenth).

Answer:

$6.8$

Problem 2: $\boldsymbol{\frac{7}{11}=\frac{18}{x + 1}}$