SOLUTION: A full box of ball bearings weighs 21 pounds. The box plus 1/3 of the ball bearings weighs 9 pounds. How much does the box alone weigh? a) 4 pounds b) 3 pounds c) 5 pounds d

Question 1190228: A full box of ball bearings weighs 21 pounds.
The box plus 1/3 of the ball bearings weighs
9 pounds. How much does the box alone weigh?
a) 4 pounds
b) 3 pounds
c) 5 pounds
d) 6 pounds
e) 2 pounds
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

This question was answered previously at this link
https://www.algebra.com/algebra/homework/Percentage-and-ratio-word-problems/Percentage-and-ratio-word-problems.faq.question.1190207.html
If you want another tutor's viewpoint, then I apologize and you can ignore the rest of the post below.

If you want another approach, then here's one possibility:
Since we're given multiple choice answers, we can go through each of them to see if they work or not.

---------------

Choice A)

If the empty box was 4 pounds, and a box full of ball bearings is 21 pounds, that gives 21-4 = 17 pounds for all the ball bearings alone.
One-third of this is (1/3)*17 = 5.667 approximately which is not a whole number. This fact allows us to cross choice A off the list.

Note how 5.667+4 = 9.667 is fairly close to 9, which seems to suggest the final answer is close to 4 pounds.

---------------

Choice B)

If the empty box was 3 pounds, then 21-3 = 18 pounds is the weight of all the bearings only.
1/3 of 18 = 6 pounds
3 + 6 = 9 pounds when the box is 1/3 full.
This shows that choice B is the answer.

---------------

Choice C through E will follow identical steps, just with different numbers of course.
The conclusion of each is that the numbers don't match up.
So we can cross these off the list as well.

Choice D will produce whole number results.
Everything else will involve decimals or fractions.

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