Question

paul ben and emma had some stickers.ben had 200 more stickers than paul.the ratio of the number of stickers paul had to the number of stickers emma had was 4:3.after ben gave 1/8 of his stickers to paul, he had 60 fewr stickers than paul.find the number of stickers

Answer 1

Given:

Paul, Ben and Emma had some stickers.

Ben had 200 more stickers than Paul.

The ratio of the number of stickers Paul had to the number of stickers Emma had was 4:3.

After Ben gave 1/8 of his stickers to Paul, he had 60 fewer stickers than Paul

To find:

The number of stickers

Solution:

Let's assume,

"P" → the no. of stickers with Paul

"B" → the no. of stickers with Ben

"E" → the no. of stickers with Emma

We have → Ben had 200 more stickers than Paul, so, we can form an equation as:

B = P + 200

⇒ B - P = 200 ...... (i)

Also, the ratio of the number of stickers Paul had to the number of stickers Emma had was 4:3,  so, we can form an equation as:

$\frac{P}{E} = \frac{4}{3}$

$\implies E = \frac{3}{4} \times P$ ..... (ii)

After Ben gave $\frac{1}{8}$ of his stickers to Paul,

Paul now had = $P + \frac{1}{8}B$

Ben now had = $B - \frac{1}{8}B - 60$

So, we can form an equation as:

$P + \frac{1}{8}B = B - \frac{1}{8}B - 60$

$\implies P + 0.125B = B - 0.125B - 60$

$\implies 60 = B - 0.125B - P - 0.125B$

$\implies 60 = 0.75B - P$ ...... (iii)

By subtracting equation (iii) from (i), we get

  B - P = 200

0.75B - P = 60

-         +      -

-------------------------

0.25B = 140

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∴ B = $\frac{140}{0.25} = \bold{560}$ ← no. of stickers Ben had

Substituting the value of B = 560 in (i), we get

B - P = 200

⇒ 560 - P = 200

⇒ P = 560 - 200

⇒ P = 360 ← no. of stickers Paul had

Substituting the value of P = 360 in (ii), we get

$\bold{E} = \frac{3}{4} \times 360 = 3 \times 90 = \bold{270 }$ ← no. of stickers Emma had

Now,

The total no. of stickers all 3 of them had,

= B + P + E

= 560 + 360 + 270

= 1190

Thus, the number of stickers Paul, Ben & Emma had → 1190.

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