SOLUTION: 2/3 of the beads are red 1/4 are yellow and the rest are blue there are 42 more red beads then blue. How much beads are there in total? I know that the answer is 72. but the proble

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Question 1190259: 2/3 of the beads are red 1/4 are yellow and the rest are blue there are 42 more red beads then blue. How much beads are there in total? I know that the answer is 72. but the problem is I am told to solve it without using algebra. And I cannot find a way to solve it without using an unknown variable.

Found 2 solutions by math_tutor2020, math_helper:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Add up the given fractions for red and yellow
2/3 + 1/4
8/12 + 3/12
11/12

11/12 of all the beads are either red or yellow, but not both.
The rest (1/12) are blue.

The fractional amounts of red and blue are
8/12
1/12
in that order

Subtract those fractional amounts
red - blue = 8/12 - 1/12 = 7/12

Then turn to the statement that there are "42 more red beads then blue", which is saying
red = blue + 42
that rearranges into the idea
red - blue = 42
I.e. the difference of the red and blue beads is 42

7/12 of the beads represents the difference of red and blue (42)
So there are (12/7)*42 = 12*6 = 72 beads total.

Or note that (7/12)*72 = 42, which is the reverse flow of logic of the previous paragraph.
(7/12)*(total) = difference in red and blue

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

2/3 + 1/4 = 8/12 + 3/12 = 11/12
Therefore, 1/12 are blue
The difference in proportion of red to blue is
8/12 - 1/12 = 7/12
So the number of beads is 42/(7/12) = 42*12 / 7 = 72

Hope this helps.
Personally, if a student is learning Algebra, I find these types of problems to be minimally helpful (it is an exercise to show how much harder problems are to solve without Algebra, but isn't that the premise for learning Algebra in the first place... that it is a powerful tool?). One doesn't need to build a house without the assistance of power tools to realize that power tools save a lot of time.