Singapore math
2/3 beads are red.
1/4 are yellow, the rest blue.
there are 42 more red beads than blue beads. how many beads altogether

Answer

The fraction of blue beads is 1 - 2/3 - 1/4 = 1/12  

If the total number of beads is t then  

red - blue = 42  

2t/3 - t/12 = 42  

therefore  

7t/12 = 42  

therefore  

t = 12x42/7 = 72

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step-by-step explanation:

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4