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

[tibi318]

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)

[stapel_eliz]

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!

[tibi318]

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?

[stapel_eliz]

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:

. . . . .

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.