The function b (x) = 2x _ 5 determines how many bags of dog food need to be purchased for an animal shelter, where x is the number of dogs at the shelter. The shelter manager uses m (b (x)) to find the amount of money to bring for the dog food purchase. The function m (x) = 3x + 1. Solve for how much money to bring when there are 10 dogs in the shelter.

15

31

46

52

The answer is 46

1. Determine the number of bags of dog food needed for 10 dogs (b (10) = ?).

2. Determine how much money is needed for the b (10) number of bags.

1. Calculate the number of bags for 10 dogs:

b (x) = 2x - 5

x = 10

b (10) = 2 · 10 - 5 = 20 - 5 = 15

Now we know that for 10 dogs, 15 bags of dog food are needed.

2. Calculate the money for 15 bags of dog food.

m (x) = 3x + 1

b (x) = 15

m (b (x)) = m (15) = 3 · 15 + 1 = 45 + 1 = 46

Now we know that for 15 bags of dog food for 10 dogs the needed amount of money is 46

B (x) = 2x - 5

m (x) = 3x + 1

m[b (x) ] = 3 [b (x) ] + 1 = 3[2x - 5] + 1 = 6x - 15 + 1 = 6x - 14

10 dogs = > x = 10 = > m (10) = 6 (10) - 14 = 60 - 14 = 46

Answer: third option, 46