Question

Cakes for dogs average $9 and are increasing $1 a year. Cakes for people average $18 and are decreasing $0.50 a year. How long before cakes for people and dogs will have the same average cost?

Answer 1

In 6 years, the average cost of cakes for dogs and people will be the same. This is calculated by setting up and solving an equation for each scenario, then finding the point where the two costs intersect.

Step-by-step explanation:

This problem is a basic algebraic word problem involving linear equations. The cost of cakes for dogs starts at $9 and increases by $1 a year, represented by the equation y = 9 + x, where y is the average cost and x is the time in years. The cost of cakes for people starts at $18 and decreases by $0.50 a year, represented by the equation y = 18 - 0.5x.

To find out when the average cost of cakes for dogs and people is the same, we set the two equations equal to each other: 9 + x = 18 - 0.5x. Solving this equation, we get x = 6. Therefore, it will be 6 years before the cakes for people and dogs will have the same average cost.

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