Questions: Solve the following proportions: a. x/5 = 10/13 x= b. 3/4 = 15/(2x) x=

Transcript text: Solve the following proportions: a. $\frac{x}{5}=\frac{10}{13}$ $x=$ $\square$ b. $\frac{3}{4}=\frac{15}{2 x}$ $x=$ $\square$ Question Help: Video $1 \square$ Video $2 \square$ Message instructor Calculator Submit Question

Solution

Solution Steps

To solve these proportions, we can use the property of cross-multiplication. For each equation, multiply the numerator of one fraction by the denominator of the other fraction and set the products equal to each other. Then, solve for the unknown variable $ x $.

Step 1: Set Up the Proportions

For each proportion, we start by setting up the equation using the given fractions.

For part (a), the equation is: \[ \frac{x}{5} = \frac{10}{13} \]
For part (b), the equation is: \[ \frac{3}{4} = \frac{15}{2x} \]

Step 2: Cross-Multiply to Solve for $ x $

Use cross-multiplication to solve for $ x $ in each equation.

For part (a), cross-multiplying gives: \[ 13x = 50 \] Solving for $ x $ yields: \[ x = \frac{50}{13} \approx 3.846 \]
For part (b), cross-multiplying gives: \[ 3 \cdot 2x = 4 \cdot 15 \] Simplifying, we have: \[ 6x = 60 \] Solving for $ x $ yields: \[ x = \frac{60}{6} = 10 \]