Question

Complete the following problems.

Amy has $50 in her lunch account. Amy spends $3 a day for lunch. Amy's mother receives a notification when Amy's
account balance reaches $5 or lower. How many lunches can Amy purchase until her mother receives a notification? And what is the equation in slope intercept form

Answer 1

Amy can purchase up to 14 lunches until her mother receives the notification. When she has the 15th lunch, the notification will be sent.

Explanation:

The balance Amy has in her lunch account is a function of the number of lunches she has consumed.

The initial balance is $50 and it decreases by $3 for every lunch Amy has. Thus, the function that models the balance in her lunch account is:

`B(x)=50-3x`

Where x is the number of lunches.

Her mother receives a notification when the balance goes at $5 or lower, thus the condition that triggers the notification is:

`B(x) \le 5`

Or, equivalently:

`50-3x\le 5`

Subtracting 50:

`-3x\le 5-50`

`-3x\le -45`

Multiplying by -1 (and flipping the sign):

`3x\ge 45`

Solving:

`x\ge45/3`

`x\ge 15`

Amy can purchase up to 14 lunches until her mother receives the notification. When she has the 15th lunch, the notification will be sent.