Mrs. Flamingo and Professor Peach are attempting to settle a score in

the conservatory. Mrs. Flamingo believes that Mr. Brown has more

candlesticks than Miss Lavender, because he has 10 more than two

thirds of the number of candlesticks that Colonel Horseradish has.

Professor Peach, however, believes that Miss Lavender has more

candlesticks, because she has three times as many as Mrs. Gray, who

has 20 fewer than Colonel Horseradish has. If Mr. Brown and Miss

Lavender actually have the same number of candlesticks, then how

many candlesticks does Colonel Horseradish have?

Colonel Horseradish has 10 candlesticks.

Step-by-step explanation:

Let x represent the number of candle sticks that Colonel Horseradish has.

Mr. Brown has 10 more than two

thirds of the number of candlesticks that Colonel Horseradish has. It means that the number of candlesticks that Mr Brown has is

2x/3 + 10- - - - - - - - -1

Miss Lavender has three times as many as Mrs. Gray, who has 20 fewer than Colonel Horseradish has. The number of candlesticks that Mrs. Gray has is

(2x/3 + 10) - 20 = 2x/3 - 10

It means that the number of candlesticks that Miss Lavender has is

3(2x/3 - 10) = 2x - 10/3 - - - - - -2

If Mr. Brown and Miss Lavender actually have the same number of candlesticks, it means that

2x/3 + 10 = 2x - 10/3

Multiplying both sides of the equation by 3, it becomes

2x + 30 = 6x - 10

6x - 2x = 30 + 10

4x = 40

x = 40/4

x = 10