Answer:
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]](https://img.qammunity.org/2021/formulas/mathematics/high-school/jdn1q7u601y6ohq76hfq37k8joa3g4vsx1.png)
Knowing that:
![\displaystyle (r)/(y)=(2)/(3) \qquad\qquad [2]](https://img.qammunity.org/2021/formulas/mathematics/high-school/f4k3g8cgt3xsnplrxjbrsvdit2wb3zxea9.png)

Multiplying the equations above:

Simplifying:
![\displaystyle (r)/(b)=(5)/(6) \qquad\qquad [3]](https://img.qammunity.org/2021/formulas/mathematics/high-school/t4w0qi23ly5cavguqyacjjvnknyey5s92m.png)
Dividing [1] by r:

Substituting from [2] and [3]:

Operating:



The fraction of the beads that are red is
