Answer:
a. Equation: [tex]70-3x=60-2.50x[/tex]
The value of gift cards will be equal after 20 30-day-periods.
b. The value of each gift card when they have equal values will be $10.
Equation: [tex]y=70-3(20)[/tex]
Step-by-step explanation:
Let be "x" the number of 30-day periods.
a. We know that Tavon has a gift card for $70 and it loses $3 for each 30-day period it is not used. This can be expressed as:
[tex]70-3x[/tex]
The other gift card for $ 60 loses $ 2.50 for each 30-day period it is not used. Then:
[tex]60-2.50x[/tex]
When the value of the gift cards are equal:
[tex]70-3x=60-2.50x[/tex]
Solve for "x":
[tex]70-3x=60-2.50x\\\\70-60=-2.50x+3x\\\\10=0.5x\\\\x=20[/tex]
Therefore, the value of the gift cards will be equal after 20 30-day-periods.
b. Let be "y" the value of each card (in dollars) when they have equal value. Choose one the expressions shown above. Let's pick the first expression [tex]70-3x[/tex]. Then:
[tex]y=70-3x[/tex]
Substitute [tex]x=20[/tex] into the equation, then:
[tex]y=70-3(20)[/tex]
Evaluate it in order to find what will be the value of each card when they have equal value:
[tex]y=70-3(20)\\\\y=10\$[/tex]
Answer:
A. [tex]70-3x=60-2.50x[/tex]
Solution: [tex]x=20[/tex]
B. The value of each card after twenty 30-day periods will be $10
Step-by-step explanation:
Let x be the number of 30-day periods.
First gift card:
Amount = $70
Lose for one 30-day period = $3
Lose for x 30-day periods = $3x
Left = $(70-3x)
Second gift card:
Amount = $60
Lose for one 30-day period = $2.50
Lose for x 30-day periods = $2.50x
Left = $(60-2.50x)
If the value of the gift cards are equal, then
[tex]70-3x=60-2.50x[/tex]
Solve this equation. First, separate variables and numbers into different sides:
[tex]-3x+2.50x=60-70\\ \\-0.50x=-10\\ \\0.5x=10[/tex]
Multiply by 10:
[tex]5x=100\\ \\x=\dfrac{100}{5}=20[/tex]
If x = 20, then
[tex]70-3x=70-3\cdot 20=70-60=10\\ \\60-2.50\cdot 20=60-50=10[/tex]
