Tavon has a gift card for $95 that loses $2 for each 30-day period it is not used. He has another gift card for $75 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?

Question

Tavon has a gift card for $95 that loses $2 for each 30-day period it is not used. He has another gift card for $75 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?

sonorous9n · Accepted Answer

For first gift card  $95 and loses $2 each day  ler x= number of days  y= value after x 30 day period  y=95−2x (1)  y=75−1.5x (2)  When gift card will have equal value 1=2  95−2x=75−1.5x→ equation to find 30-day period until gift card has equal value  95−75=(2−1.5)x  0.5x=20  x=40  a) 30 day period value of gift card will be equal.  after 40×30=1200 days  Answer: 40  b) Value of card when equal  1) y=95−2x  y=95−2×40  y=15  for (2)  y=75−1.5x  y=75−1.5×40  y=15  Answer: $15 each card will have $15 as equal value.

Philip Williams · Accepted Answer

Gift Card 1 (C=GC1) has a value of $95−Time ⋅(−$230 days) Mathematically, lets set T for a time increment of 30 days. 1T=30 days. So we can state the value of GC1, in increments of 30 days, as GC1=95−T⋅($230 days). And so, GC2=75−T⋅($1.530 days) We want to know the value of T when the cards are equal in value. So for what value of T does GC1=GC2? 95−T⋅2=75−T⋅1.5, where T is in increments of 30 days. Rearranging, 20=0.5T T=40 After 40 30-day periods (1200 days), both cards should have equal value (assuming you don&#039;t use them in the meantime). Let&#039;s check it: Card 1 after 40 periods: $95−(40⋅$2)=$15 Card 2: $75−(40⋅1.5)=$15.

alenahelenash · Accepted Answer

The first part to solving this equation is to put one fact against another and set them to be equal each other. Gift card one starts at $95 and loses $2 per month, while gift card two starts at $75 and loses $1.50 per month. $95−$2(months)=$75−$1.5(months)If we move dollars to the left and months to the right, we&#039;ll get: $20=$.5(x) Dividing both sides by the coefficient of x ($.5) will yield the number of months until both gift cards are of equal value. Substituting that number of months for x in our original equation will yield the dollar amount.(After 40 months, each of the cards will be $15.)

Tavon has a gift card for $95 that loses $2 for each 30-day period it is not used. He has another gi

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