Simultaneous equations!

Algebra Level 2

The difference between two numbers is 8. If 2 is added to the bigger number, the result will be 3 times the smaller number. Find these two numbers, and submit your answer as the sum of these two numbers.


The answer is 18.

Soha Farhin Pine Pine by Soha Farhin Pine Pine , 18, Bangladesh

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1 solution

Sam Bealing
Jul 23, 2016

Let the smaller number be x x and thr bigger number y y we know:

{ y = x + 8 y + 2 = 3 x ⟹ ( x + 8 ) + 2 = 3 x ⟹ x = 5 \begin{cases} y =x+8 & \\ y+2=3x & \end{cases} \implies (x+8)+2=3x \implies x=5

x = 5 , y = 5 + 8 = 13 x=5,y=5+8=13

So the answer is:

13 + 5 = 18 13+5=\boxed{\boxed{18}}

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