Questions: Solving Proportions Solve each of the proportions below. Be sure to write your answer as an equation in simplified form. Proportion 8/-32 = -t/56 18/108 = 4/(z+2) 10/(3 m) = 50/45 (2 w+5)/-5 = (-4 w+34)/-10

Solving Proportions
Solve each of the proportions below. Be sure to write your answer as an equation in simplified form.
Proportion
8/-32 = -t/56
18/108 = 4/(z+2)
10/(3 m) = 50/45
(2 w+5)/-5 = (-4 w+34)/-10

Transcript text: Solving Proportions Solve each of the proportions below. Be sure to write your answer as an equation in simplified form. \begin{tabular}{|c|} \hline Proportion \\ \hline$\frac{8}{-32}=\frac{-t}{56}$ \\ $\frac{18}{108}=\frac{4}{z+2}$ \\ $\frac{10}{3 m}=\frac{50}{45}$ \\ $\frac{2 w+5}{-5}=\frac{-4 w+34}{-10}$ \\ \hline \end{tabular}

Solution

Solution Steps

Solution Approach

For the first proportion $\frac{8}{-32}=\frac{-t}{56}$, cross-multiply to find the value of $t$.
For the second proportion $\frac{18}{108}=\frac{4}{z+2}$, cross-multiply and solve for $z$.
For the third proportion $\frac{10}{3m}=\frac{50}{45}$, cross-multiply and solve for $m$.

Step 1: Solve for $ t $

Starting with the proportion: \[ \frac{8}{-32} = \frac{-t}{56} \] Cross-multiplying gives: \[ 8 \cdot 56 = -32 \cdot (-t) \] This simplifies to: \[ 448 = 32t \] Dividing both sides by 32 results in: \[ t = \frac{448}{32} = 14 \]

Step 2: Solve for $ z $

Next, consider the proportion: \[ \frac{18}{108} = \frac{4}{z+2} \] Cross-multiplying yields: \[ 18(z + 2) = 108 \cdot 4 \] This simplifies to: \[ 18z + 36 = 432 \] Subtracting 36 from both sides gives: \[ 18z = 396 \] Dividing by 18 results in: \[ z = \frac{396}{18} = 22 \]

Step 3: Solve for $ m $

Now, we look at the proportion: \[ \frac{10}{3m} = \frac{50}{45} \] Cross-multiplying results in: \[ 10 \cdot 45 = 50 \cdot 3m \] This simplifies to: \[ 450 = 150m \] Dividing both sides by 150 gives: \[ m = \frac{450}{150} = 3 \]