Answer:
- 65 -3x = 55 -2.5x
- 20 periods
- $5
Explanation:
The value of the first card starts at $65 and decreases by $3 for each of x periods. Its value is ...
65 -3x
The value of the second card starts at $55 and decreases by $2.50 for each of x periods. Its value is ...
55 -2.5x
The equation that can be used to find x that makes the values equal is ...
65 -3x = 55 -2.5x
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The solution can be found by adding 3x-55 to both sides of this equation.
10 = 0.5x
Multiplying by 2 gives ...
20 = x
After 20 30-day periods. the cards will have the same value.
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The value after 20 periods is ...
65 -3×20 = 65 -60 = 5
Both cards will have a value of $5 when they have the same value.