Fraction questions

Question

3 girls used the same number of beads to make necklaces. Devi used 2/5 of her beads, Esther used 3/4 of hers and Farah used 2/3 of hers. They had a total of 1440 beads at first. How many beads did each girl use?

Answer 1

Davi used  2/5

Esther used 3/4

Farah used 2/3

 

Let D = Davi's original # beads

Let E = Esther's original # beads

Let F = Farah's original # beads

 

D + E + F = 1440

 

(2/5)D = (3/4)E = (2/3)F

 

From (2/5)D = (2/3)F

D = (5/3)F

 

From (3/4)E = (2/3)F

E = (8/9)F

 

Substitute those back into D + E + F = 1440

(5/3)F + (8/9)F + F = 1440

(15/9)F + (8/9)F + (9/9)F = 1440

(32/9)F = 1440

F = 1440(9/32)

F = 405 beads

 

D = (5/3)F = 405(5/3) = 675 beads

 

E = (8/9)F = 405(8/9) = 360 beads

 

Davi had 675 beads

Esther had 360 beads

Farah had 405 beads

 

Davi used (2/5)(675) = 270 beads

Esther used (3/4)(360) = 270 beads

Farah used (2/3)(405) = 270 beads

 

Answer checks and each girl used 270 beads