Respuesta :
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the terms with a variable
Let x be the amount she earns per hour as a cashier
Let y be the amount she earns per hour as a cook
STEP 2: Interpret the statements in the question as seen below:
[tex]\begin{gathered} 12x+10y=306 \\ 14x+22y=512 \end{gathered}[/tex]STEP 3: Solve the simultaneous equation using elimination to get x and y
[tex]\begin{gathered} 12x+10y=306---(1) \\ 14x+22y=512----(2) \\ \\ \text{ Multiply equation 1 by 14 and equation 2 by 12} \\ 14\lbrack12x+10y=306\rbrack\Rightarrow168x+140y=4284----(3) \\ 12\lbrack14x+22y=512\Rightarrow168x+264y=6144----(4) \\ \\ \text{Subtract equation 4 from equation 3} \\ 168x\text{ cancels 168x, we have;} \\ 140y-264y=4284-6144 \\ -124y=-1860 \\ \text{Divide both sides by -124} \\ \frac{-124y}{-124}=\frac{-18600}{-124} \\ y=15 \end{gathered}[/tex]STEP 4: Solve any of equation to get the value of x
[tex]\begin{gathered} \text{From equation 1} \\ 12x+10y=306 \\ y=15\text{, By substitution;} \\ 12x+10(15)=306 \\ 12x+150=306 \\ \text{Subtract 150 from both sides} \\ 12x+150-150=306-150 \\ 12x=156 \\ \text{Divide both sides by 12} \\ \frac{12x}{12}=\frac{156}{12} \\ x=13 \end{gathered}[/tex]Since x represents the amount she earns as a cashier, hence She earns $13 per hour as a cashier
