charlottes weekly paycheck is based on the number of hours worked during the week and on the weekend. if she…

charlottes weekly paycheck is based on the number of hours worked during the week and on the weekend. if she works 13 hours during the week and 14 hours on the weekend, she earns $250.90. if she works 15 hours during the week and 8 hours on the weekend, she earns $204.70. how much more does charlotte earn per hour on the weekends than she earns during the week? round to the nearest cent.\n$0.40\n$1.90\n$2.30\n$8.10

charlottes weekly paycheck is based on the number of hours worked during the week and on the weekend. if she works 13 hours during the week and 14 hours on the weekend, she earns $250.90. if she works 15 hours during the week and 8 hours on the weekend, she earns $204.70. how much more does charlotte earn per hour on the weekends than she earns during the week? round to the nearest cent.\n$0.40\n$1.90\n$2.30\n$8.10

Answer

Explanation:

Step1: Definir variables

Sea $x$ la paga por hora durante la semana y $y$ la paga por hora en el fin - de - semana. Podemos establecer un sistema de ecuaciones a partir de la información dada: $$\begin{cases}13x + 14y=250.90\15x + 8y=204.70\end{cases}$$

Step2: Multiplicar las ecuaciones para eliminar una variable

Multiplicamos la segunda ecuación por $\frac{7}{4}$ para que el coeficiente de $y$ sea el mismo que en la primera ecuación. La segunda ecuación $15x + 8y=204.70$ multiplicada por $\frac{7}{4}$ es: $\frac{7}{4}(15x + 8y)=\frac{7}{4}\times204.70$ $\frac{105}{4}x+14y = 358.225$

Step3: Restar las ecuaciones

Restamos la primera ecuación $13x + 14y=250.90$ de la ecuación resultante de Step2: $(\frac{105}{4}x+14y)-(13x + 14y)=358.225 - 250.90$ $\frac{105}{4}x+14y - 13x-14y=107.325$ $\frac{105}{4}x-13x=107.325$ $\frac{105x - 52x}{4}=107.325$ $\frac{53x}{4}=107.325$ $x=\frac{107.325\times4}{53}$ $x = 8.1$

Step4: Encontrar el valor de $y$

Sustituimos $x = 8.1$ en la primera ecuación $13x+14y = 250.90$: $13\times8.1+14y=250.90$ $105.3+14y=250.90$ $14y=250.90 - 105.3$ $14y=145.6$ $y=\frac{145.6}{14}=10.4$

Step5: Calcular la diferencia

Calculamos la diferencia entre $y$ y $x$: $y - x=10.4 - 8.1 = 2.3$

Answer:

$2.30$