math algerbra 9th grade

Question

a hairdresser is considering ordering a certain shampoo. company a chargers $4 per bottle plus a $10 handling fee per order. company b charges $3 per bottle plus a $25 handling fee per order. how many bottles must the hair dresser buy to justify using company b

Answer 1

10 + 4x = 25 + 3x

10 + x = 25

x = 15

15 bottles is the same price:

10 + 4*15 = 10 + 60 = 70 = 25 + 3*15 = 25+45

plugging in test values

x=0 ---> 10 < 25

x=15 ---> 70 = 70

x=16 ---> 10 + 4*16 = 10 + 64 = 74 > 25 + 3* 16 = 25 + 48 = 73

# of bottles x Plan A cost plan B cost

0 10 25

15 70 70

16 74 73

Plan B is cheaper when # of bottles is MORE than 15.