Question

Please can I have an explanation also, I am terrible at these kinds of questions!

Q- A bag contain 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.

Answer 1

The fraction of the beads that are red is

Explanation:

Algebraic Expressions

A bag contains red (r), yellow (y), and blue (b) beads. We are given the following ratios:

r:y = 2:3

y:b = 5:4

We are required to find r:s, where s is the total of beads in the bag, or

s = r + y + b

Thus, we need to calculate:

`\displaystyle (r)/(r+y+b) \qquad\qquad [1]`

Knowing that:

`\displaystyle (r)/(y)=(2)/(3) \qquad\qquad [2]`

`\displaystyle (y)/(b)=(5)/(4)`

Multiplying the equations above:

`\displaystyle (r)/(y)(y)/(b)=(2)/(3)(5)/(4)`

Simplifying:

`\displaystyle (r)/(b)=(5)/(6) \qquad\qquad [3]`

Dividing [1] by r:

`\displaystyle (r)/(r+y+b)=\displaystyle (1)/(1+y/r+b/r)`

Substituting from [2] and [3]:

`\displaystyle (r)/(r+y+b)=\displaystyle (1)/(1+3/2+6/5)`

Operating:

`\displaystyle (r)/(r+y+b)=\displaystyle (1)/((10+3*5+6*2)/(10))`

`\displaystyle (r)/(r+y+b)=\displaystyle (10)/(10+15+12)`

`\displaystyle (r)/(r+y+b)=\displaystyle (10)/(37)`

The fraction of the beads that are red is
`\mathbf{(10)/(37)}`