Question

Tavon has a gift card for $ 50 that loses $ 2 for each​ 30-day period it is not used. He has another gift card for $ 40 that loses $ 1.50 for each​ 30-day period it is not used. a. Write and solve an equation for the number of​ 30-day periods until the value of the gift cards will be equal. b. What will the value of each card be when they have equal​ value?

Answer 1

To find the number of 30-day periods until the value of the gift cards will be equal, we set up and solve an equation. The value of each card will be $10 when they have equal value.

Step-by-step explanation:

To solve this problem, we can set up an equation to represent the value of each gift card over time and find when they will be equal.

Let x be the number of 30-day periods that have passed. After x periods, the value of the first gift card will be $50 - $2x, and the value of the second gift card will be $40 - $1.50x.

Setting the two expressions equal, we get:

$50 - $2x = $40 - $1.50x

Simplifying the equation, we have:

$10 = $0.5x

Dividing both sides by $0.5, we get:

x = 20

So, after 20 periods (or 20 months), the value of each gift card will be equal.

To find the value of each card at that point, we can substitute x = 20 into one of the expressions. Let's use the first gift card:

Value = $50 - $2(20) = $50 - $40 = $10

Therefore, when they have equal value, each gift card will be worth $10.

Answer 2

So we know that month 1: gift card 1: 50$ gift card 2: 40$

month 2: gift card 1: 48 gift card 2: 38.50

month 3: gift card 1: 46 gift card 2: 37

month 4: gift card 1: 44 gift card 2: 35.5

month 5: gift card 1: 42 gift card 2: 34

month 6: gift card 1: 40 gift card 2: 32.5

month 7: gift card 1: 38 gift card 2: 31

month 8: gift card 1: 36 gift card 2: 29.5

month 9: gift card 1: 34 gift card 2: 28

month 10: gift card 1: 32 gift card 2: 26.5

month 11: gift card 1: 30 gift card 2: 25

month 12: gift card 1: 28 gift card 2: 23.5

month 14: gift card 1: 26 gift card 2: 22

month 15: gift card 1: 24 gift card 2: 20.5

month 16: gift card 1: 22 gift card 2: 19

month 17: gift card 1: 20 gift card 2: 17.5

month 18: gift card 1: 18 gift card 2: 16

month 19: gift card 1: 16 gift card 2: 14.5

month 13: gift card 1: 14 gift card 2: 13

month 13: gift card 1: 12 gift card 2: 11.5

month 14 gift card 1: 10 gift card 2: 10

MONTH 14 THEY ARE EQUAL