Question #70147

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Answer 1 · 2017-06-27T01:52:21

Alexis's salary is $$ 160$ $$160$ .

We can represent their respective salaries as follows:

Gary's salary $= x$ $=x$

Alexis's salary $= 2 \frac{1}{2} \times x = \frac{5}{2} \times x = \frac{5 x}{2}$ $=2 1/2xxx=5/2xxx=(5x)/2$

James's salary $= (x + 18)$ $=(x+18)$

Their total daily salary is $306$ $306$ , so we can write:

$x + \frac{5 x}{2} + (x + 18) = 306$ $x+(5x)/2+(x+18)=306$

Open the brackets and simplify.

$x + \frac{5 x}{2} + x + 18 = 306$ $x+(5x)/2+x+18=306$

$2 x + \frac{5 x}{2} + 18 = 306$ $2x+(5x)/2+18=306$

Multiply all terms by $2$ $2$ and then simplify.

$(2 \times 2 x) + (2 \times \frac{5 x}{2}) + (2 \times 18) = 306 \times 2$ $(2xx2x)+(2xx(5x)/2)+(2xx18)=306xx2$

$(4x)+(1cancel2xx(5x)/(1cancel2))+(36)=612$

$4x+5x+36=612$

$9x+36=612$

Subtract $36$ from each side.

$9x+36-36=612-36$

$9x=576$

Divide both sides by $9$ .

$(9x)/9=576/9$

$(1cancel9x)/(1cancel9)=64$

$x=64$

Thus, Gary's daily salary is $$64$ .

Alexis's salary $=(5x)/2=(5xx64)/2=(5xx32cancel64)/(1cancel2)=5xx32=160$

Thus, Alexis's salary is $$160$ .

James's salary $=(x+18)=(64+18)=82$

Thus, James's salary is $$82$ .

To check:

$64+160+82=306$