Question

Two-third 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 altogether ?
Please show each and every step
please answer fast please

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.

Answer 2

Concept Introduction:-

It could take the shape of a word or a number representation of the quantity's arithmetic value.

Given Information:-

We have been given that two-third 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

To Find:-

We have to find that beads are altogether

Solution:-

According to the problem

r $=$ number of red

b $=$ number of blue

y $=$ number of yellow

r $=$ b $+ 35$ or b = r $- 35$ and I suppose r $- b = 35$

Fraction that are blue

$1 - ( 2/3 + 1/4 )\\1 - ( 8/12 + 3/12 )\\1 - ( 11/12 )\\b = 1/12$

Since $y$ is $1/4$ and $y = 3/12$, $y = 3b$

Since $r$ is $2/3$ and $r = 8/12$, $r = 8b$

Combine $r = b + 35$ with $r = 8b$

This means that $b + 35= 8b$

Subtract $b$ from each side

$35 = 7b\\5 = b$

So we have $b = 5$ , $y = 3b$ and $r = 8b$

Since $b + y + r = total$

By substituting

$5 + 3(5) + 8(5) = total\\5 + 15 + 40 = 60$

Final Answer:-

The correct answer is $60$ beads.

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