Question

You have a cafeteria card worth $50.after you buy lunch on Monday, it's value is $46.75. After you buy lunch on Tuesday, it's value is $43.50. Writes an explicit formula to represent the amount of money left on the card as an arithmetic sequence. What is the value of the card after you buy 12 lunches?

Answer 1

Y=50-3.25X after 12 lunches it would have a value of 11$

Answer 2

Answer:  The sequence is M(n) = $50 - $3.25*n where n is the number of lunches you bought, and after 12 lunches the amount left in your card is $11

Step-by-step explanation:

You initially had $50 on your card.

After one lunch, you had $46,75

This means that the cost of the lunch was C = $50 - $46.75 = $3.25

After the second lunch, you had $43.50 in your card, this means that the cost this time was c2 = $46.75 - $43.50 = $3.25

Then the arithmetic sequence that represents the amount of money in your card can be written as:

M(n) = $50 - $3.25*n

where n is the number of lunches that you bought.

If you want to calculate the amount of money after 12 lunches, you need to replace n by 12:

M(12) = $50 - $3.25*12 = $11