Shares

Algebra Level 1

If $510 is to be divided among A, B, and C such that A gets 2 3 \frac{2}{3} of what B gets and B gets 1 4 \frac{1}{4} what C gets.

What are their shares respectively?

$0 , $0 , $0 $110 ,$80, $320 $60, $90, $360 $10 , $50 , $150 $40 , $70 , $200

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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2 solutions

Mohammad Khaza
Jul 18, 2017

suppose, C gets x

so, B gets = x 4 \frac {x}{4} and A gets= x 6 \frac {x}{6}

now, x + x 4 + x 6 x+ \frac {x}{4} + \frac {x}{6} = 510 510

or, 12 x + 3 x + 2 x 12 \frac {12x+3x+2x}{12} = 510 510

or, 17 x 17x = 6120 6120

or, x x = 360 360 = C C

so, 2nd option is the answer as their shares are written accordingly.

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Marta Reece
May 11, 2017

C = 4 B = 4 × 3 2 A = 6 A C=4B=4\times\frac{3}{2}A=6A

This relationship is satisfied if C = 12 x , B = 3 x , A = 2 x C=12x,B=3x, A=2x

(I picked 12 because it is the lowest common multiple of 4 and 6.)

In total A + B + C = 2 x + 3 x + 12 x = 17 x = $ 510 A+B+C=2x+3x+12x=17x=\$510

x = $ 30 x=\$30 , therefore A = $ 60 , B = $ 90 , C = $ 360 A=\$60, B=\$90, C=\$360

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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