During a one-month promotional campaign, tiger films gave either a free dvd rental or a 12-serving box of microwave popcorn to new members. it cost the store $1 for each free rental and $2 for each box of popcorn. a total of 67 new members were signed up and the store's cost for the incentives was $96. how many of each incentive were given away?

The answer is

Free Rental given = r = 38

Box of popcorn given = b = 29

Explanation:

Let,

Free Rental given = r

Box of popcorn given = b

Given that,

Cost of Free Rental = $1

Cost of Box of popcorn = $2

Total Cost of incentive = $96

Total incentives given = 67

Free Rental given+Box of popcorn given = Total incentives given

r+b=67

r=67-b ... (1)

(Free Rental given) x (Cost of Free Rental) + (Box of popcorn given) x (Cost of Box of popcorn) = Total Cost of incentive

(r x 1) + (b x 2) = 96

r + 2b = 96 ... (2)

Put the value of r in (2) from (1)

r+2b=86 ... (2)

67-b+2b = 96

67+b = 96

b = 96-67

b = 29

Put the value of b in (1)

r = 67-b ... (1)

r = 67-29

r = 38

Free Rental given = r = 38

Box of popcorn given = b = 29