Andrea C. answered • 10/12/14

Together, we can get you there! Masters degree - 20 years experience.

Minasaka R.

asked • 10/12/14The difference between two-thirds of a number and one-sixth of the same number is 75. What is the number?

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Andrea C. answered • 10/12/14

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(246)
Together, we can get you there! Masters degree - 20 years experience.

Hi there,

Writing a "word sentence" into a "number sentence" part of the problem is sometimes the most difficult for a student to write.

"The Difference Between" means that you will subtract the next two things in the problem...so where it says "The difference between "2/3 of a number and 1/6 of the same number"...you put a minus sign where the "and" is.

When a word problem tells you that you are going to write "a number," you will write a letter (also known as a variable). So where the problem says, "The difference between 2/3 of 'a number'"...you write a letter like 2/3 x.

Putting the whole problem together...word for word, number for number, symbol for symbol...you get the following.

(I write out the "number sentence" above the "word sentence" so I can see that I remembered everything).

2/3 x - 1/6 x = 75

Difference between two-thirds of a number and one-sixth of the same number is 75. What is the number?

Kye D. answered • 10/12/14

Tutor

New to Wyzant
Sir Tutor Excellence

Let X = the number

2/3 X - 1/6 X = 75

Multiply everything by 6.

4X - X = 450

3X = 450

X = 150

Check:

2/3(150) - 1/6(150) = 75

100 - 25 = 75

75 = 75

(2/3)x - (1/6)x = 75 Multiply both sides of the equal sign by 6 to clear the fractions

-> 6((2/3)x - (1/6)x)) = 75(6) Distribute the 6

-> 4x - x = 450 Combine like term

-> 3x = 450 Divide by 3 on both sides of the equal sign

-> x = 150

test

(2/3)(150) - (1/6)(150) = 75

-> 100 - 25 = 75

-> 75 = 75

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