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25 WORD PROBLEMS THAT LEAD TO EQUATIONS WITH FRACTIONS HERE ARE SOME WORD PROBLEMS that lead to equations with fractions. Example 1. Half of a number, added to a fifth of three less than the number, is equal to two thirds the number. What is the number? Solution. As always, let x answer the question; let x be that number.
Here is the equation:
The LCM of denominators is 30. And upon clearing of fractions, we have
Example 2. This problem is from a classical Hindu text on algebra from the 9th century. During an amorous struggle, the lady's pearls broke. Half of the pearls fell onto the floor; a fourth rolled under a chair; a sixth fell into her lap; and three pearls remained on the strand. How many were there originally on the strand? Solution. Let x be that total number. And let us account for them all. First, we will clear the equation of fractions. The LCM of 2, 4, and 6 is 12. We will multiply every term by 12, and cancel the denominators:
There were originally 36 pearls on the strand. Example 3. One number is three times another. The sum of their reciprocals is 4. What are the two numbers? Solution. Let x be the first number. Then the other is three times that: 3x. The problem states that the sum of their reciprocals is 4:
(Note that the sum of their reciprocals -- 3 + 1 -- does equal 4.) Problem 1. Half of a number added to its third part, is eight less than the number. What is the number? To see the equation, pass your mouse over the colored area. The equation is:
Problem 2. Three fifths of a number, plus 8, is equal to the number. What is the number? Here is the equation:
Problem 3. Half of a number, plus a fifth of two less than the number, is four less than the number. What is the number? Here is the equation:
Problem 4. Melissa went shopping and spent half of her money on shoes, a third on a blouse, a tenth to take her boyfriend to lunch, and she came home with $12. How much did she start out with? Here is the equation:
Problem 5. One number is four times another. The sum of their
Let x be the first number. Then the other is 4x. Here is the equation:
These are the two numbers. Problem 6 If the same number is added to the numerator and
Here is the equation:
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