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# help

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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.

May 27, 2020
edited by Guest  May 27, 2020
edited by Guest  May 27, 2020
edited by Guest  May 27, 2020

#1
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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 May 27, 2020