Before we start solving this question, we should make an equation that describes this question:

Let's assume that the number is 'x'. Then, the product of the number and 3 would be 3x.

Sum of the number and 5 would be:

x+5

and twice this would be:

2(x+5)

=2x + 10

Now, as the question says, the product of the number with 3 equals twice the sum of the number with 5. SO:

3x = 2x + 10

Let's solve for x:

3x = 2x + 10

3x - 2x = 10

x = 10

The number is 10.

To prove that it is 10, let's apply it to the question. The product of 10 and 3 is 30.

The sum of 10 and 5 is 15. Twice this value is 15x2= 30. Thus, we have proved that the product of the number with 3 (30) equals twice the sum of the number with 5 (30).

Let's assume that the number is 'x'. Then, the product of the number and 3 would be 3x.

Sum of the number and 5 would be:

x+5

and twice this would be:

2(x+5)

=2x + 10

Now, as the question says, the product of the number with 3 equals twice the sum of the number with 5. SO:

3x = 2x + 10

Let's solve for x:

3x = 2x + 10

3x - 2x = 10

x = 10

The number is 10.

To prove that it is 10, let's apply it to the question. The product of 10 and 3 is 30.

The sum of 10 and 5 is 15. Twice this value is 15x2= 30. Thus, we have proved that the product of the number with 3 (30) equals twice the sum of the number with 5 (30).