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Chapter 6: Problem 72

Solve each proportion and check. \(\frac{2}{y-5}=\frac{3}{y+6}\)

Short Answer

Expert verified
The solution to the proportion is \(y = 27\)

Step by step solution

01

Cross Multiply

To get rid of the fractions, cross multiply which means multiply the numerator of the first fraction with the denominator of the second fraction, set equal to the numerator of the second fraction multiplied by the denominator of the first fraction. This results in \(2(y+6) = 3(y-5)\)
02

Distribute and Simplify

Distribute within the brackets to simplify. The equation becomes \(2y+12 = 3y-15\). Afterwards, combine like terms to isolate \(y\) by subtracting \(2y\) from both sides to get \(y = 27\).
03

Check the solution

Substitute \(y = 27\) back into the original equation and simplify which gives \(\frac{2}{22}=\frac{3}{33}\) which simplifies to \(\frac{1}{11}=\frac{1}{11}\). This is correct because both fractions are equal.

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