# Question 70147

Alexis's salary is $160. #### Explanation: We can represent their respective salaries as follows: Gary's salary$= x$Alexis's salary$= 2 \frac{1}{2} \times x = \frac{5}{2} \times x = \frac{5 x}{2}$James's salary$= \left(x + 18\right)$Their total daily salary is $306$, so we can write: $x + \frac{5 x}{2} + \left(x + 18\right) = 306$Open the brackets and simplify. $x + \frac{5 x}{2} + x + 18 = 306$$2 x + \frac{5 x}{2} + 18 = 306$Multiply all terms by $2$and then simplify. $\left(2 \times 2 x\right) + \left(2 \times \frac{5 x}{2}\right) + \left(2 \times 18\right) = 306 \times 2$$\left(4 x\right) + \left(1 \cancel{2} \times \frac{5 x}{1 \cancel{2}}\right) + \left(36\right) = 612$$4 x + 5 x + 36 = 612$$9 x + 36 = 612$Subtract $36$from each side. $9 x + 36 - 36 = 612 - 36$$9 x = 576$Divide both sides by $9$. $\frac{9 x}{9} = \frac{576}{9}$$\frac{1 \cancel{9} x}{1 \cancel{9}} = 64$$x = 64$Thus, Gary's daily salary is $64.
Alexis's salary$= \frac{5 x}{2} = \frac{5 \times 64}{2} = \frac{5 \times 32 \cancel{64}}{1 \cancel{2}} = 5 \times 32 = 160$
Thus, Alexis's salary is $160. James's salary$= \left(x + 18\right) = \left(64 + 18\right) = 82$Thus, James's salary is $82#.
$64 + 160 + 82 = 306$