# Twins Diana and Riana are each 6 years older than their younger brother Kyle. Together, their 3...

## Question:

Twins Diana and Riana are each {eq}6 {/eq} years older than their younger brother Kyle. Together, their {eq}3 {/eq} ages total of {eq}21 {/eq} years.

How old is Kyle?

## Verbal Statement Into the Equation:

We can translate a verbal statement into an equation by using algebraic operations. Here, we use + for "more than", - for "less than, multiplication for "times" etc. We can then solve it using algebraic operations on both sides of the equation.

Let us assume the ages of each of the twins Diana and Riana be {eq}x {/eq} years.

Let us assume the age of their younger brother Kyle be {eq}y {/eq} years.

The problem says, "Twins Diana and Riana are each 6 years older than their younger brother Kyle".

So we get:

$$x= y+6 \,\,\,\,\,\,\,\rightarrow (1)$$

The problem says, "the sum of their 3 ages is {eq}21 {/eq} years".

So we get:

$$x+ x +y = 21 \\[0.3cm] 2x+y=21 \\[0.3cm] \text{Substitute x=y+6 using (1). Then we get,} \\[0.3cm] 2(y+6)+y=21 \\[0.3cm] 2y+12 +y =21 \\[0.3cm] 3y+12= 21 \\[0.3cm] \text{Subtracting 12 from both sides}, \\[0.3cm] 3y=9 \\[0.3cm] \text{Dividing both sides by 3}, \\[0.3cm] y=3$$

Therefore, Kyle is {eq}\boxed{\mathbf{3 \text{ years}}} {/eq} old. 