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Chapter 6: Problem 71

Solve each proportion and check. \(\frac{y+10}{10}=\frac{y-2}{4}\)

Short Answer

Expert verified
The solution to the proportion is \( y = 10 \)

Step by step solution

01

Apply Cross-Multiplication

Cross-multiply the fractions to eliminate denominators, which yields: \( (y+10) * 4 = 10 * (y-2) \)
02

Simplify the Equation

Expand and simplify the above cross-multiplication equation. It yields: \( 4y + 40 = 10y - 20 \)
03

Solve for y

To isolate \(y\), combine like terms by subtracting \(4y\) from both sides of the equation and then adding 20 to both sides. This gives us: \( 60 = 6y \). Divide both sides of the equation by 6 to find the value of \(y\), which gives us: \( y = 10 \)
04

Check Your Solution

To verify the solution, substitute \(y = 10\) into the original proportion and check whether both ratios are equal. This gives \( \frac{10+10}{10} = \frac{10-2}{4} \). After simplifying, we can confirm that both sides of the equation are equal (2 = 2), which verifies that y = 10 is indeed the solution to the proportion

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