Question

Leyla and her sister Maryam are excited to begin saving for a new bike they can share. Their aunt said that if they saved up enough money, she would split the cost with them and pay for half. The new bike will cost $110 total.

The girls concluded that they would have just enough if they saved the money from 2 days’ worth of Leyla’s paper route and 3 days’ worth of Maryam’s dog walking job. Maryam has to work a little more because her dog walking job pays $5 less than Leyla’s paper route. How much do the paper route and dog walking jobs each earn per day?

Answer 1

• paper route: $14 per day
• dog walking: $9 per day

Explanation:

You want to know the pay for a paper route and dog walking if 2 days' paper route pay and 3 days' dog walking pay will total half of $110, while dog walking pays $5 less than the paper route.

Setup

Let p represent the pay for a day's pay for the paper route. Then (p-5) is the day's pay for dog walking. The total pay is ...

2p +3(p -5) = 110/2

Solution

Simplifying the equation, we have ...

5p -15 = 55

p -3 = 11 . . . . . . . . divide by 5

p = 14 . . . . . . . . add 3

p -5 = 14 -5 = 9 . . . . . pay for dog walking

The paper route and dog walking pay 14 and 9 dollars per day, respectively.

__

Additional comment

We could write two equations, and solve by substitution. We would get the same single equation by doing that. In this solution method, it works well to let the variable represent the largest contributor (highest pay).

We could also solve the two equations by any of several other methods. The attached graph shows the solution by graphing.