# Given the equation 6=-s+77, what is the value of 1+5(77-s)?

Oct 22, 2016

We want to first figure out what the value of $s$ is, so let's do that.

If $6 = - s + 77$, we can rearrange the formula to get $s = 71$:

$6 = - s + 77$
$6 + s = 77$
$s = 71$

Now that we know the value of $s$, we can substitute it into the formula $1 + 5 \left(77 - s\right)$.

Let's sub in $s = 71$ and solve it.

$1 + 5 \left(77 - 71\right)$
$1 + 5 \left(6\right)$
$1 + 30 = 31$

Oct 22, 2016

$1 + 5 \left(77 - s\right) = 31$

#### Explanation:

The trick to reducing the solution work for this question is spotting that one is a part repeat of the other.

Let the unknown value be $x$ then

$x = 1 + 5 \left(77 - s\right) \ldots \ldots \ldots \ldots E q u a t i o n \left(1\right)$
$6 = - s + 77. \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left(2\right)$

Change the order of equation(2) giving

$x = 1 + 5 \left(77 - s\right) \textcolor{w h i t e}{.} \ldots \ldots \ldots . E q u a t i o n \left(1\right)$
6=77-s color(white)(.)......................Equation(2_a)color(red)(" "larr"part repeat"

Substitute for $77 - s$ in Equation(1) using $E q u a t i o n \left({2}_{a}\right)$

So Equation(1) becomes:

$x = 1 + 5 \left(77 - s\right) \text{ "->" } x = 1 + 5 \left(6\right)$

$x = 31$