Sam and Tammy are brothers. Their combined age is \(20,\) and Tammy is \(4\) years older than Sam. What are Sam and Tammy’s ages?
Let Sam and Tammy’s ages be \(x\) years and \(y\) years respectively.
Then, since their combined age is \(20,\) we have:
\(x+y=20 ~ ~ ~ ~ ~ —-(1)\)
Tammy is \(4\) years older than Sam.
\(\therefore \text{Tammy’s age} = 4 ~\text{years} + \text{Sam’s age}\)
\(\therefore y=x+4~ ~ ~ ~ ~ —-(2)\)
\((1)\) and \((2)\) form a system or a pair of linear equations in the variables \(x\) and \(y.\) Solve this system by substituting the value of \(y\) from \((2)\) in \((1).\)
\(\implies x+(x+4)=20\)
\(\implies 2x + 4 = 20\)
\(\implies 2x = 20-4 = 16\)
\(\implies x = \dfrac{16}{2}= 8\)
Thus, Sam is \(8\) years old.
Since \(y=x+4,\) this means that \(y=8+4 = 12.\)
Thus, Tammy is \(12\) years old.