# What is the fraction of x's?

Red letters and blue letters are used in a game. Some of the letters are X. All the other letters are Y. The ratio of the number of red letters to blue letters is 2:5. The ratio of the number of red x's to red y's is 1:3. The ratio of blue x's to blue y's is 3:1. Work out what fractions of all the letters are x's.

### 1 Answer

- atsuoLv 62 months ago
Let the number of red Xs be RX and the number of red Ys be RY .

RX:RY = 1:3 , so RY = 3RX and RX+RY = 4RX .

Let the number of blue Xs be BX and the number of blue Ys be BY .

(RX+RY):(BX+BY) = 2:5 , so BX+BY = (5/2)(RX+RY) = (5/2)4RX = 10RX .

BX:BY = 3:1 , so BX = (3/4)(BX+BY) = (3/4)10RX = (15/2)RX and

BY = (1/4)(BX+BY) = (1/4)10RX = (5/2)RX .

The answer is

(RX+BX)/((RX+RY)+(BX+BY))

= (RX+(15/2)RX)/(4RX+10RX)

= (17/2)RX/(14RX)

= 17/28

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