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Question 703287: The sum of a number and 60, divided by 8, results in one half of the number. Find the number
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! "The sum of a number and 60..." A sum of two or more things means those things are being added together. The numbers we have are 60 and an unknown number, which we'll use a variable for. Thus, we translate from this fragment of the sentence the expression x + 60.
"...divided by 8..." What is being divided by 8? The thing previously before it, or the sum of the two numbers we have mentioned. Thus, we know that if the sum is x + 60, and if the sum is being divided by 8, we have (x+60)/8.
"...results in one half of the number." What number are we talking about? The same unknown number we used in the first step. With this piece of information, we can write our equation: (x+60)/8 = x/2. (The sum of a number and 60, x + 60, is divided by 8, (x+60)/8, which results in 1/2 the number we do not know, (x+60)/8 = x/2). Now we can solve for that unknown number using algebraic manipulation.
(x+60)/8 = x/2
2*(x+60)/8 = 2*x/2 (multiply each side by 2)
[2(x+60)]/8 = x (simplify)
(2x+120)/8 = x (distributive property in the numerator)
8*(2x+120)/8 = 8*x (multiply each side by 8)
2x + 120 = 8x (simplify)
2x - 2x + 120 = 8x - 2x (subtract each side by 2x)
120 = 6x (simplify)
120/6 = 6x/6 (divide each side by 6)
20 = x (simplify)
x = 20 (answer).
We can check by plugging x back in and see if it meets the requirement mentioned in the problem. This number must have a sum with 60 when divided by 8 equals 1/2 of the original number. Or, (20+60)/8 = 20/2, 80/8 = 20/2, 10 = 10. We have the correct number: x = 20.
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