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Red letters and blue letters are used in a game.
Some of the letters are X.
All the other letters are Y.
XY
XY
The ratio of the number of red letters to the number of blue letters is 2:5
The ratio of the number of red Xs to the number of red Ys is 1:3
The ratio of the number of blue Xs to the number of blue Ys is 3 : 1
Work out what fraction of all the letters are Xs.​

Red letters and blue letters are used in a gameSome of the letters are XAll the other letters are YXYXYThe ratio of the number of red letters to the number of b class=

Respuesta :

Answer:

85/140

Step-by-step explanation:

2:5 = 7

140 letters/7=20 each.

2=40  (2*20)

5=100  (5*20)

10/30= Red

75/25=Blue

10+75=85/140

[tex]\frac{17}{28}[/tex] of all the letters are Xs.

What is ratio?

'A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one.'

According to the given problem,

Ratio of red letters to blue letters = 2 : 5

Ratio of red Xs to red Ys = 1 : 3

Ratio of blue Xs to blue Ys = 3 : 1

Number of red letters = [tex]\frac{2}{2+5}[/tex]

                                    = [tex]\frac{2}{7}[/tex]

Number of Xs = [tex]( \frac{2}{7} * \frac{1}{1+3}) + [( 1-\frac{2}{7})*\frac{3}{3+1})][/tex]

                       = [tex](\frac{2}{7} *\frac{1}{4})+(\frac{5}{7}*\frac{3}{4} )[/tex]

                       = [tex]\frac{1}{4}+\frac{15}{28}[/tex]

                       = [tex]\frac{2+15}{28}[/tex]

                       = [tex]\frac{17}{28}[/tex]

Hence, we can conclude,    [tex]\frac{17}{28}[/tex] of all letters are Xs.

Learn more about ratio here: https://brainly.com/question/13419413

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