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The explicit formula that represents the amount of money left on the card

is a = 53.25 - 3.25n

The value of the card after 12 lunches is $14.25

Step-by-step explanation:

The explicit formula of the arithmetic sequence is a = a + (n - 1)d, where

In the question

∵ You have 50 dollars

∵ The money left after lunch on Monday is 46.75 dollars

∵ The money left after lunch on Tuesday is 43.50 dollars

∴ The terms of the sequence are 50, 46.75, 43.50

∵ 46.75 - 50 = -3.25

∵ 43.50 - 46.75 = -3.25

→ That means there is a common difference between each 2 terms

∴ d = -3.25

∵ a = 50

→ Substitute the values of a and d in the rule above

∴ a = 50 + (n - 1)(-3.25)

→ Simplify it

∵ a = 50 + -3.25(n) + -3.25(-1)

∴ a = 50 - 3.25n + 3.25

→ Add the like terms

∴ a = 53.25 - 3.25n

∴ The explicit formula that represents the amount of money left on the

   card is a = 53.25 - 3.25n

∵ n is the number of lunches

∴ n = 12

→ Substitute n by 12 to find the amount of money left on the card

∵ a = 53.25 - 3.25(12)

∴ a = 14.25

∴ The value of the card after 12 lunches is $14.25

all teachers

step-by-step explanation: