the sum of the ages of Sam and Tomas is 27 years. Seven years ago, Tomas was three years more than one- fourth as old as Sam. find there present age.
+26367 The sum of the ages of Sam and Tomas is 27 years.
Seven years ago, Tomas was three years more than one- fourth as old as Sam.
Find there present age.
x = sam age
y = thomas age
\(\begin{array}{|rclcrcl|} \hline x+y &=& 27 \quad \text{or} \quad \mathbf{y = 27-x} \\\\ \mathbf{y-7} &=& \mathbf{\dfrac{1}{4}(x-7) + 3} \\ y &=& \dfrac{1}{4}(x-7) + 3 +7 \\\\ y &=& \dfrac{1}{4}(x-7) + 10\quad | \quad y = 27-x \\\\ 27-x &=& \dfrac{1}{4}(x-7) + 10 \\\\ -x &=& \dfrac{1}{4}(x-7) + 10-27 \\\\ -x &=& \dfrac{1}{4}(x-7) -17 \\\\ x + \dfrac{1}{4}(x-7) &=& 17 \quad | \quad *4 \\\\ 4x + x-7 &=& 4*17 \\\\ 5x &=& 4*17 +7 \\\\ 5x &=& 75 \\\\ \mathbf{x} &=& \mathbf{15} \\ \hline \\ \mathbf{y} &=& \mathbf{27-x} \\ y &=& 27-15 \\ \mathbf{y} &=& \mathbf{12} \\ \hline \end{array}\)
sam is 15 and thomas is 12
