Question

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

Answer 1

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

Answer 2

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