# The second of two numbers is 6 times the first. The sum is 77. How do you find the numbers?

Mar 25, 2018

$a = 11$, $b = 66$
You should set up two equations.

#### Explanation:

The second of two numbers is $6$ times the first. This means that you must multiply the first number by $6$ to get the second number.

$\implies$$6 a = b$

The sum is 77.

$\implies$$a + b = 77$

You want to set the equations equal to each other, so subtract $a$ from both sides:

$\implies$$b = 77 - a$

Now set them equal:

$\implies$$6 a = 77 - a$

Add $a$ to both sides:

$\implies$$7 a = 77$

Divide by $7$

$\implies$$a = 11$

Now plug this into the first equation:

$\implies$$6 \left(11\right) = b$ $\to$ $66 = b$

So $a = 11$ and $b = 66$.