Answer:
- Alice: y = 11 +1x
- Benito: y = 1 +3x
- 16 cards after 5 days
Explanation:
Alice starts with 11 cards and buys 1 per day. Benito starts with 1 card and buys 3 per day. You want equations for Alice and Benito that describe the number of cards they have (y) in terms of the number of days (x) that have passed. you also want graphs of these equations and when and where the numbers of cards are the same.
Equations
It really should be no mystery that the number of cards will be the sum of the initial number and the product of the number of days and the number of cards acquired each day:
Alice: y = 11 +1x
Benito: y = 1 +3x
Graph
See the attachment for a graph and the point where the graphs intersect:
x = 5, y = 16 . . . . . both have 16 cards after 5 days.
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Additional comment
The equations are defined for negative x- and y-values, but in the context of this problem the only values that make sense are ones where x ≥ 0 and y > 0.