Ratio Numbers Explained: Sum Calculation

This problem asks us to find the sum of the first and fourth number when four numbers are given in a specific ratio and their total sum is known.

Representing Ratio Numbers

We are given that four numbers are in the ratio $1:2:3:4$. Let the numbers be $1x$, $2x$, $3x$, and $4x$, where $x$ is a common multiplier.

Calculating the Common Multiplier

The problem states that the sum of these four numbers is $16$. We can write this as an equation:

$1x + 2x + 3x + 4x = 16$

Combine the terms on the left side:

$ (1+2+3+4)x = 16 $

$ 10x = 16 $

Now, solve for $x$ by dividing both sides by $10$:

$ x = \frac{16}{10} $

$ x = 1.6 $

Finding the First and Fourth Numbers

Now that we know the value of $x$, we can find the first and fourth numbers:

• First number: $1x = 1 \times 1.6 = 1.6$
• Fourth number: $4x = 4 \times 1.6 = 6.4$

Calculating the Sum of First and Fourth Numbers

The question asks for the sum of the first and fourth numbers. Add the values we found:

Sum = First number + Fourth number

Sum = $1.6 + 6.4$

Sum = $8.0$

So, the sum of the first and fourth numbers is $8$.