Question

The sum of three numbers is 97. The third number is 3 times the second. The second number is 8 more than the first. What are the numbers? A) First number: B) Second number: C) Third number:

Answer 1

Answer:

A) First number: 13

B) Second number: 21

C) Third number: 63

Step-by-step explanation:

Let x, y and z be 1st, 2nd and 3rd numbers respectively.

We have been given that sum of three numbers is 97. We can represent this information in an equation as:

$x+y+z=97...(1)$

The 3rd number is 3 times the second. We can represent this information in an equation as:

$z=3y...(2)$

The second number is 8 more than the first. We can represent this information in an equation as:

$y=x+8...(3)$

Substituting equation (3) in equation (2), we will get:

$z=3(x+8)$

Substituting $z=3(x+8)$ and $y=x+8$ in equation (1), we will get:

$x+x+8+3(x+8)=97$

$x+x+8+3x+24=97$

$5x+32=97$

$5x+32-32=97-32$

$5x=65$

$\frac{5x}{5}=\frac{65}{5}$

$x=13$

Therefore, the first number is 13.

Now, we will substitute $x=13$ in equation (3) as:

$y=21$

Therefore, the second number is 21.

Now, we will substitute $y=21$ in equation (2) as:

$z=3(21)$

$z=63$

Therefore, the third number is 63.