Question

Use cross products to solve each proportion.

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

Short answer

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

Step-by-step solution

- 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 $ad=bc$

- Substitution

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

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

- 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

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