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:. . . . .
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.