Home

#### Algebra and Pre-Algebra Lessons

Algebra 1 | Pre-Algebra | Practice Tests | Algebra Readiness Test

#### Algebra E-Course and Homework Information

Algebra E-course Info | Log In to Algebra E-course | Homework Calculator

#### Formulas and Cheat Sheets

Formulas | Algebra Cheat Sheets

# Algebra Word Problem

by Abby Hope
(Henderson, NC)

The product of two fractions is 1/9. The larger fraction divided by the smaller fraction is 4. What is the sum of the two fractions? Express your answer as a common fraction.

### Comments for Algebra Word Problem

Average Rating

 Sep 29, 2010 Rating Algebra Word Problem by: Karin Hi Abbey, This is a great problem! Let's first identify the variables. You know that you are dealing with 2 numbers and one is larger than the other. Let x = the larger number Let y = the smaller number Now we can write two equations: The product of the two numbers is 1/9. Product means multiply. xy = 1/9 The larger number divided by the smaller number is 4. x/y = 4 So, we have: xy = 1/9 and x/y = 4 Since we have two equations, we actually have a system of equations. We need to solve the system. I am going to use the substitution method. Step 1: Solve one of the equations for a variable. I will solve x/y = 4 for x. Multiply both sides by y. y(x/y)= 4y x = 4y Now, we'll substitute 4y for x into the equation: xy = 1/9 4y(y) = 1/9 4y^2 = 1/9 Now divide by 4 on both sides. 4y^2/4 = 1/9 / 4 y^2 = 1/36 Now take the square root of both sides and you end up with: y = 1/6 Now substitute 1/6 for y into the equation x = 4y x = 4y x = 4(1/6) x = 4/6 x = 2/3 So, the two numbers are 1/6, & 2/3. Now let's check before we finish the problem: xy = 1/9 (1/6)(2/3) = 1/9 2/18 = 1/9 1/9 = 1/9 AND x/y = 4 2/3 / 1/6 = 4 2/3 * 6/1 = 4 12/3 = 4 4 = 4 Yes, our answers are correct. So, now the question asked for the sum of the numbers, so we must add the numbers together. 1/6 + 2/3 = 5/6 The correct answer is 5/6 Hope this helps, Karin xy = 1/9 (1/6)(2/3) =

Top of the Page

Custom Search