Question

Andy has twice as many marbles as Pandy, and Sandy has half as many has Andy and Pandy put together. If Andy has 75 marbles more than Sandy, how many does each of them have.

Answer 1

Hint:
In number problems, there are some clues about one or more numbers, and we can use these clues to form an equation that represents the problem mathematically.
To solve this question read the question carefully, choose a variable to represent the number. Translate the problem into an equation. Solve the equation and check the answer using the equation formed.
Here, we assume that the number of marbles with Pandy is x. According to the question, we will form an equation for the number of marbles with Andy and Sandy in terms of x. On solving all the equations we will get the value of x and can determine the number of marbles with each of them.

Complete step by step solution:
Let the number of marbles with Pandy = x
According to the question the number of marbles which Andy has is twice as many as Pandy.
Therefore, Andy has 2x marbles.
Now, it is also given that Sandy has half as many as Andy and Pandy together.
So, Sandy has $\dfrac{1}{2}\left( {x + 2x} \right) = \dfrac{{3x}}{2}marbles$
Now, Andy has 75 marbles more than Sandy
∴$2x = \dfrac{{3x}}{2} + 75$
$
2x - \dfrac{{3x}}{2} = 75 \\
\dfrac{{4x - 3x}}{2} = 75 \\
x = 2 \times 75 \\
x = 150 \\
$
Hence, number of marbles with Pandy = x = 150
The number of marbles with Andy = 2x
$2 \times 150 = 300marbles$
And Sandy has $\dfrac{{3x}}{2}marbles$
$\dfrac{{3 \times 150}}{2} = 225marbles$
Hence, Pandy has 150 marbles, Andy has 300 marbles and Sandy has 225 marbles.

Note:
Linear equation in one variable is the easiest way to solve this question. To solve these types of questions, reasoning must be performed based on common sense knowledge and the information provided by the source problem. Some word problems ask to find two or more numbers. We will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.