## ratio: Mary has 11N marbles and cathy has 7N marbles so we h

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### ratio: Mary has 11N marbles and cathy has 7N marbles so we h

hi i am stuydiyng for a gre exam and i am having trouble figuring out a fraction/ratio problem. it states:

Mary has 11N marbles and cathy has 7N marbles so we have a ratio of 11:7. after the gift, Mary will have 11N - 3 marbles. after receiving 3 marbles , cathy will have 7N + 3 marbles. the new ration in terms of N, after the gift is: (11N -3)/(7N + 3) and the numerical value of this ratio is 16/11. How do we get 16/11 from (11N -3)/ (7N +3)
tibi318

Posts: 2
Joined: Wed May 20, 2009 2:46 am

tibi318 wrote:Mary has 11N marbles and cathy has 7N marbles so we have a ratio of 11:7. after the gift, Mary will have 11N - 3 marbles. after receiving 3 marbles , cathy will have 7N + 3 marbles. the new ration in terms of N, after the gift is: (11N -3)/(7N + 3) and the numerical value of this ratio is 16/11. How do we get 16/11 from (11N -3)/ (7N +3)

Please provide the full and exact text of the exercise.

Thank you!

stapel_eliz

Posts: 1718
Joined: Mon Dec 08, 2008 4:22 pm

### Re: ratio: Mary has 11N marbles and cathy has 7N marbles so we h

Mary and Cathy have marbles in the ratio 11:7. If Mary gifts away 3 of her marbles to Cathy, then the new ratio of marbles will be 16:11. How many more marbles does Mary have than Cathy does after the gift?
tibi318

Posts: 2
Joined: Wed May 20, 2009 2:46 am

tibi318 wrote:Mary and Cathy have marbles in the ratio 11:7. If Mary gifts away 3 of her marbles to Cathy, then the new ratio of marbles will be 16:11. How many more marbles does Mary have than Cathy does after the gift?

Ah; that's a bit different!

The original ratio was 11 to 7. The final ratio was 16 to 11. Use the variable you chose, we have:

. . . . .original: 11N to 7N

. . . . .final: 11N - 3 to 7N + 3

Also:

. . . . .final: 16 to 11

Use these two "final" ratios to set up the proportion:

. . . . .$\frac{11N\, -\, 3}{7N\, +\, 3}\, =\, \frac{16}{11}$

Cross-multiplying gives:

. . . . .11(11N - 3) = 16(7N + 3)

. . . . .121N - 33 = 112N + 48

. . . . .9N = 81

Solve for the value of N, and thus for the numbers of marbles.

stapel_eliz

Posts: 1718
Joined: Mon Dec 08, 2008 4:22 pm