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

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

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