Question

Question 12 (10 points)Students love to put ranch dressing on everythig, so Elvira needs to keep plenty in stock. The students eat about 2.25 gallons of ranch each day! Elvira started the school year with 130 gallons of ranch dressing. She needs to have at least 20 gallons left when she reorders to have enough in stock until the new order comes. For how many days will her ranch dressing supply last before she needs to reorder?A. Write and solve an inequality that models this situation.B. Describe in words the quantities that would work in this situation.C. Write your answer in both interval and set notation.

Answer 1

We will formulate an equation that gives us the number of gallons left after x days.

So, we know that there are 130 gallons at the beginning and every day there are 2.25 gallons less. Therefore, the equation is:

y = 130 - 2.25x

Where y is the number of gallons left. Additionally, She needs to have at least 20 gallons left when she reorders to have enough in stock until the new order comes. It means that y needs to be at least 20:

$\begin{gathered} y\ge20 \\ 130-2.25x\ge20 \end{gathered}$

Now, to know how many days will her ranch dressing supply last before she needs to reorder we need to solve it for x as:

$\begin{gathered} 130-2.25x\ge20 \\ 130-2.25x+2.25x\ge20+2.25x \\ 130\ge20+2.25x \\ 130-20\ge20+2.25x-20 \\ 110\ge2.25x \\ \frac{110}{2.25}\ge\frac{2.25x}{2.25} \\ 48.89\ge x \end{gathered}$

So, she needs to reorder before 48.89 days or in the interval (0, 48.89) days.

Answer: 48.89 days

A.

$\begin{gathered} 130-2.25x\ge20 \\ x\leq48.89\text{ days} \end{gathered}$

B. She needs to reorder before 48.89 days. It means that she has from 0 to 48.89 days to reorder if she wants enough in stock until the new order comes

C. Interval notation: (0, 48.89 )

Set notation: { x | 0 ≤ x ≤ 48.89}