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

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Answer 1 · 2018-03-25T02:40:24

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

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

$\Rightarrow$ $=>$ $6 a = b$ $6a=b$

The sum is 77.

$\Rightarrow$ $=>$ $a + b = 77$ $a+b=77$

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

$\Rightarrow$ $=>$ $b = 77 - a$ $b=77-a$

Now set them equal:

$\Rightarrow$ $=>$ $6 a = 77 - a$ $6a=77-a$

Add $a$ $a$ to both sides:

$\Rightarrow$ $=>$ $7 a = 77$ $7a=77$

Divide by $7$ $7$

$\Rightarrow$ $=>$ $a = 11$ $a=11$

Now plug this into the first equation:

$\Rightarrow$ $=>$ $6 (11) = b$ $6(11)=b$ $\to$ $->$ $66 = b$ $66=b$

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