Problem Solving

The ratio of black rabbits to white rabbits in the hat magician Uri Geller was 7:9. After he turned 3 of the black rabbits to white rabbits the two quantities were equal. What was the original total number of rabbits?

A) 20 (B) 32 (C) 48 (D) 64 (E) 90


The ratio of statues to paintings in Ann's villa was 3:10. After 30 paintings were stolen from Ann's house the ratio of statues to paintings became 12:25. What was the original number of statues in Ann's house?

(A) 18 (B) 24 (C) 30 (D) 48 (E) 80


In Erica's garden the ratio of purple tulips to red tulips is 3:5, and the ratio of white roses to yellow roses is 2:3. If the number of white roses in Erica's garden is twice the number of purple tulips, what is the ratio of yellow roses to red tulips?

(A) 5:1 (B) 10:1 (C) 2:7 (D) 9:5 (E) 4:9

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Please post each problem in a separate thread.
I believe that the first problem should read as follows:

TeddyBonham wrote:The ratio of black rabbits to white rabbits in the hat of magician Uri Geller was 7:9. After he turned 3 of the white rabbits to black rabbits, the two quantities were equal. What was the original total number of rabbits?

A) 20 (B) 32 (C) 48 (D) 64 (E) 90

Since the number of rabbits switching from white to black is small, the total number of rabbits must also be small.

Strategy:
TEST small values such that B:W = 7:9.
Options:
B=7, W=9
B=14, W=18
B=21, W=27.
Use this list to calculate options for the next statement.

After he turned 3 of the white rabbits to black rabbits the two quantities were equal.
New B = 7+3 = 10, new W = 9-3 = 6.
New B = 14+3 = 17, new W = 18-3 = 15.
New B = 21+3 = 24, new W = 27-3 = 24.

The option in red works.
Thus:
Original total = 21+27 = 48.

The correct answer is C.

The ratio of black rabbits to white rabbits in the hat of magician Uri Geller was 7:9. After he turned 3 of the white rabbits to black rabbits, the two quantities were equal. What was the original total number of rabbits?

A) 20 (B) 32 (C) 48 (D) 64 (E) 90

And there's always good 'ol algebra.

Initially:

Black: 7x
White: 9x
Total: 16x


If 3 white rabbits are turned black, our new scenario will be

Black: 7x+3
White: 9x -3

We're told the two quantities above are equal.
7x + 3 = 9x - 3
6= 2x
3 = x

16x = 16*3 = 48