Question 218709: Hi - I have a pretty simple problem from my homework that I just can't seem to figure out. It's not a huge deal, but it's annoying me that I can get all the others but this seemingly simple problem has got me stumped!
The problem: A quantity, 2/3 of it, 1/2 of it, and 1/7 of it, added together, equals 33. What is the quantity?
Here's what I've tried, and checked repeatedly, but don't see the error... (I'm sure it's something simple, which is so annoying!)
let x = the quantity
2/3x + 1/2x + 1/7x = 33 [the problem I created from the word problem]
(42)2/3x + (4y662)1/2x +90-0-0-0-090-87797 (42)1/7x = 33(42) [multiply by common denominator to clear fractions]
28x + 21x + 6x = 1,386
55x = 1,386
x = 1,68758758587587578
The book tells me that the correct answer is 1,386/97! Where in the world does the 97 come from??
Many thanks in advance for all the great help you guys give on here!
Answer by MathTherapy(10555)   (Show Source):
You can put this solution on YOUR website! A quantity, 2/3 of it, 1/2 of it, and 1/7 of it, added together, equals 33. What is the quantity?
Let the quantity be Q
Since the quantity,  of it,  of it, and  of it, added together equals 33, then we'll have:
42Q + 28Q + 21Q + 6Q = 1,386 ----- Multiplying equation by its LCD, 42
97Q = 1,386
Q =  , which can be expressed this way or as a decimal by dividing 1,386 by 97
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