Question

Two-thirds of the beads in a box are red, one-fourth are yellow and the rest are blue. there are 35
more red beads than blue beads. How many beads are there altogether? ​

Answer 1

Answer:

Let the total no. of beads be x.

2x / 3 are red, x / 4 are yellow and the rest are blue.

Let's find the part of blue beads among the all.

\begin{gathered} x - (\frac{2x}{3} + \frac{x}{4}) \\ \\ = x - (\frac{8x + 3x}{12}) \\ \\ = x - \frac{11x}{12} = \frac{x}{12} \end{gathered}

x−(

3

2x

+

4

x

)

=x−(

12

8x+3x

)

=x−

12

11x

=

12

x

∴ One - twelfth of the beads are blue.

The no. of red beads is 35 more than that of blue beads, i. e.,

\begin{gathered} \frac{2x}{3} - \frac{x}{12} = 35 \\ \\ = \frac{24x - 3x}{36} = 35 \\ \\ = \frac{21x}{36} = 35 \\ \\ 21x = 35 * 36 = 1260 \\ \\ x = \frac{1260}{21} = 60 \end{gathered}

3

2x

−

12

x

=35

=

36

24x−3x

=35

=

36

21x

=35

21x=35∗36=1260

x=

21

1260

=60

∴ There are 60 beads altogether.

Step-by-step explanation:

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