(a)
Subtract 8 from 2 : | 2 - 8 | |
Multiply by 5 : |
| 5(2 - 8) |
Add \(\frac12\)(12 * 8 - 24) : | 5(2 - 8) + \(\frac12\)(12 * 8 - 24) |
So
our result = 5(2 - 8) + \(\frac12\)(12 * 8 - 24) = -30 + 36 = 6
(b)
Notice that no matter what number we chose to begin with,
we can calculate our result with this equation:
result = 5(2 - x) + \(\frac12\)(12x - 24) , where x is the number we chose.
Let's simplify this and solve for x .
result = 10 - 5x + 6x - 12
result = x - 2
Add 2 to both sides of the equation.
result + 2 = x
In other words...
the number we chose = our result + 2 .
To find the number we chose, MathWizard adds 2 to our result.