Thread: Cost word problem

To shampoo a small dog at Pretty Pooches costs $20. When the owner of Pretty Pooches increases the price to have a small dog shampooed, the number of small dogs shampooed per day decreases. The expression ax+b represents the number of small dogs shampooed in 1 day whenever the price is x dollars per dog. The number of small dogs shampooed per day was 12 when the price given originally was in effect. The number of small dogs shampooed per day decreases by 2 for every $5 increase in price. What are the values of a and b?

How can I show that a = -2/5 and b = 20?

You are given that "The number of small dogs shampooed per day was 12 when the price given originally ($20) was in effect". If d= ax+ b (d being number of dogs shampooed at x dollars per dog) that says 12= a(20)+ b. You are also told that "The number of small dogs shampooed per day decreases by 2 for every $5 increase in price". So if the price increases to 20+ 5= $25, the number of dogs shampooed will decrease to 12- 2= 10 dogs. That means that 10= a(25)+ b. Solve the two equations 20a+ b= 12 and 25a+ b= 10. (You can immediately eliminate b by subtracting the first equation from the second.)