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Please help me with this question, thanks.​

Please help me with this question, thanks.​-example-1

2 Answers

7 votes

Answer:

Benny has 50 marbles

Explanation:

Let Benny's marbles be x

∴ Ahmad's marbles = x - 35


(1)/(5) x = (2)/(3)(x - 35)


(x)/(5) = (2x - 70)/(3)

∴3x = 5(2x - 70)

∴3x = 10x - 350

∴350 = 10x - 3x

∴7x = 350

∴ x = 50

Benny has 50 marbles

User Malwinder Singh
by
8.6k points
2 votes

Hello!

Answer:


\Large \boxed{\sf 50}

Explanation:

Let x be the number of Ahmad's marbles. So:

Ahmad =
\sf x

Benny =
\sf x + 35

We also know:


\sf (1)/(5) ~of~ Benny's~ marbles = (2)/(3) ~of ~Amhad's ~marbles

Replace Benny's marbles and Ahmad's marbles by
\sf x and
\sf x + 35.

Therefore, we have this equation:


\sf (1)/(5) ~of~ x+35 = (2)/(3) ~of ~x

We have just to solve this equation to find the number of Ahmad's marbles for then to find the number of Benny's marbles.

Simplify both sides:


\sf (x+35)/(5) = (2x)/(3)

Multiply both sides by 3:


\sf (x+35)/(5) * 3 = (2x)/(3) * 3

Simplify both sides:


\sf (3(x+35))/(5) = 2x

Simplify the fraction:


\sf (3x+105)/(5) = 2x

Multiply both sides by 5:


\sf (3x+105)/(5) * 5 = 2x * 5

Simplify both sides:


\sf 3x+105= 10x

Subtract 3x from both sides:


\sf 3x+105-3x= 10x -3x

Simplify both sides:


\sf 105 = 7x

Divide both sides by 7:


\sf (105)/(7) = (7x)/(7)

Simplify both sides:


\sf x = 15

So the number of Ahmad's marbles is 15.

To find the number of Benny's marbles, we know:

Benny =
\sf x + 35

So we have just to replace x by 15:

Benny =
\sf 15 + 35 = 50

So the number of Benny's marbles is 50.

Check:


\sf (1)/(5) ~of~50 = (1 * 50 )/(5) = (50)/(5) = 10


\sf (2)/(3) ~of ~15= (2 * 15 )/(3) = (30)/(3) = 10

So the equation
\sf (1)/(5) ~of~ x+35 = (2)/(3) ~of ~x is verified if x = 15.

User Yfeldblum
by
8.1k points

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