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.

Answer and Explanation:

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.


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