Q64. - Algebra 2

Question

Use cross products to solve each proportion.

$\frac{x}{5}=\frac{x+1}{8}$

Step-by-Step Solution

Answer

Given proportion is simplified to $x=\frac{5}{3}$

Step 1 - Cross product between two proportions

Let $\frac{a}{b}$ and $\frac{c}{d}$ be two equal proportions that is $\frac{a}{b}=\frac{c}{d}$

Then cross product is defined as multiplication of denominator of one proportion with the numerator of other proportion, that is $ad=bc$

Step 2 - Substitution

Substitute x for a, 5 for b, $x+1$ for c, and 8 for d into $ad=bc$ gives

$x\times 8=5\times \left(x+1\right)$

Step 3 - Simplify x × 8 = 5 × x + 1

To simplify this expression multiply both the numbers of right side and then simplify to group the coefficient of variable and then divide it from coefficient as shown below

 $\begin{array}{c}8x=5x+5\\ 8x-5x=5\\ 3x=5\\ x=\frac{5}{3}\end{array}$