Question

Angelo's mother put $50 on his lunch card. He spends the same amount

each day for lunch. Write a function that gives the amount of money
remaining on Angelo's lunch card over time.
1. Complete the table to show how much Angelo has left on his card
after each day.
Days
0
1
2
3
Money Remaining
44.75
39.5

Answer 1

Angelo spends $5.25 on lunch each day. A function to describe the money remaining on his card is Money Remaining = $50 - $5.25x. Each subsequent day, $5.25 is deducted from the balance.

Step-by-step explanation:

To determine the function that describes the amount of money remaining on Angelo's lunch card over time, we first need to find out how much he spends each day. Based on the information given, the amount Angelo has left after one day is $44.75, and after two days it's $39.50. This suggests that Angelo spends $5.25 per day on lunch ($50 - $44.75 on day 1 and $44.75 - $39.50 on day 2). The function representing the amount of money remaining on the card after x days would be the starting amount of $50 minus the daily spend multiplied by x days.

The function can be written as: Money Remaining = $50 - $5.25x

Complete Table:

• Day 0: $50.00
• Day 1: $44.75
• Day 2: $39.50
• Day 3: $34.25

Each day, he will spend another $5.25, and the table can be updated accordingly to show the money remaining over time.

Answer 2

Given that Angelo spends the same amount every day from the amount in

the lunch card, the function of the amount remaining is a linear function.

The constant rate of change of the function is; -5.25

The two ordered pairs used to find the constant rate of change are; (1, 44.75) and (2, 39.5)

Reasons:

The amount Angelo's mother put on the lunch card = $50

A possible table of values to the question is presented as follows;

Required:

The constant rate of the function that gives the amount remaining from the

amount Angelo's mother put on his lunch card.

Solution:

The two ordered pairs that can be used to find the slope or constant rate of change are;

(x₁, y₁) = (1, 44.75), and (x₂, y₂) = (2, 39.5)

With the above two ordered pairs, we have the constant rate of change of the function given as follows;

The constant rate of change for the function that gives the amount remaining in the lunch card is; -5.25