Final answer:
To find the number of days when the two doggie day cares will be the same price, set up an equation, simplify, and solve.
Step-by-step explanation:
To find the number of days when the two doggie day cares will be the same price, we need to set up an equation.
Let x be the number of days.
For the first doggie day care, the price is $40x + $50.
For the second doggie day care, the price is $20x + $150.
Setting these two expressions equal to each other, we get: 40x + 50 = 20x + 150.
Simplifying and solving for x, we find that x = 5.
Therefore, after 5 days, the two doggie day cares will be the same price.