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Please can I have an explanation, I am terrible at these kinds of questions! Q- A bag contains red, yellow and blue beads. The ratio of red beads to yellow beads is 2:3 The ratio of yellow beads to blue beads is 5:4 Work out what fraction of the beads are red.

Respuesta :

MrRoyal

Answer:

[tex]Red = \frac{10}{37}[/tex]

Step-by-step explanation:

Given

[tex]Red:Yellow = 2 : 3[/tex]

[tex]Yellow: Blue = 5 : 4[/tex]

Required

Determine the fraction of Red

First, we need to link the given ratios.

Since yellow is present in both ratios, we start by making the ratio of yellow equal in both ratios

Multiply this ratio by 5

[tex]Red:Yellow = 2 : 3[/tex]

This becomes

[tex]Red:Yellow = 10 :15[/tex]

Similarly, multiply this ratio by 3

[tex]Yellow: Blue = 5 : 4[/tex]

This becomes

[tex]Yellow:Blue =15:12[/tex]

At this point, we have:

[tex]Red:Yellow = 10 :15[/tex] and [tex]Yellow:Blue =15:12[/tex]

Combine

[tex]Red:Yellow:Blue = 10:15:12[/tex]

The fraction is then calculated as:

[tex]Red = \frac{Red}{Red +Yellow + Blue}[/tex]

This gives

[tex]Red = \frac{10}{10+15+12}[/tex]

[tex]Red = \frac{10}{37}[/tex]

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