addison earns a fixed hourly rate working as a sales clerk. if she works on a holiday, she earns a different…

addison earns a fixed hourly rate working as a sales clerk. if she works on a holiday, she earns a different hourly rate than she earns on a regular day. in one week, she earns $188.50 by working 5 hours on a holiday and 16 hours during regular days. a different week, she earns $254.00 by working 8 hours on a holiday and 20 hours during regular days. how much more is addisons holiday hourly rate than her regular hourly rate?\n$2.00\n$8.50\n$10.50\n$19.00

addison earns a fixed hourly rate working as a sales clerk. if she works on a holiday, she earns a different hourly rate than she earns on a regular day. in one week, she earns $188.50 by working 5 hours on a holiday and 16 hours during regular days. a different week, she earns $254.00 by working 8 hours on a holiday and 20 hours during regular days. how much more is addisons holiday hourly rate than her regular hourly rate?\n$2.00\n$8.50\n$10.50\n$19.00

Answer

Answer:

A. $2.00

Explanation:

Step1: Set up equations

Let $x$ be the holiday - hourly rate and $y$ be the regular - hourly rate. We have the system of equations: $$\begin{cases}5x + 16y=188.5\8x + 20y=254\end{cases}$$

Step2: Multiply the first equation

Multiply the first equation by 4 and the second equation by 5 to make the coefficients of $x$ the same for elimination. The first equation becomes $20x+64y = 754$. The second equation becomes $40x + 100y=1270$.

Step3: Eliminate $x$

Multiply the first new - equation by 2: $40x+128y = 1508$. Subtract the second new - equation ($40x + 100y=1270$) from it: $(40x + 128y)-(40x + 100y)=1508 - 1270$. $28y=238$, so $y=\frac{238}{28}=8.5$.

Step4: Find $x$

Substitute $y = 8.5$ into the first original equation $5x+16\times8.5 = 188.5$. $5x+136 = 188.5$. $5x=188.5 - 136=52.5$. $x=\frac{52.5}{5}=10.5$.

Step5: Calculate the difference

The difference between the holiday and regular hourly rates is $x - y$. $x - y=10.5-8.5 = 2$.