the function b(x)=2 x-5 determines how many bags of dog food needs 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 here there are 10 dogs in the shelter? Help!
first find bx by substituting in 10 for x in the equation for the number of dogs. so... bx=2(10) - 5 = 15. we need 15 bags of dog food. now substitute in 15 for x in the m(x) equation 3(15)+1= 46. $46 to purchase 15 bags of dog food for 10 dogs.
hope this helps.
To solve for how much money to bring when there are 10 dogs in the shelter, we need to substitute the value of x=10 into the given functions.
First, we substitute x=10 into b(x)=2x-5:
b(x) = 2x-5
b(10) = 2(10)-5
b(10) = 20-5
b(10) = 15
So, when there are 10 dogs in the shelter, we need to purchase 15 bags of dog food.
Next, we substitute b(10) = 15 into m(x) = 3x+1:
m(x) = 3x+1
m(b(10)) = 3(15)+1
m(b(10)) = 45+1
m(b(10)) = 46
Therefore, when there are 10 dogs in the shelter, the shelter manager needs to bring $46 for the dog food purchase.
To solve this problem, we need to follow these steps:
Step 1: Start with the given information.
The function b(x) = 2x - 5 tells us how many bags of dog food to purchase based on the number of dogs x.
The function m(x) = 3x + 1 tells us how much money to bring based on the quantity x.
Step 2: Substitute the value of x into b(x) to find the number of bags needed.
Substituting x = 10 into b(x), we have: b(10) = 2(10) - 5.
Evaluating this expression gives us b(10) = 20 - 5 = 15.
So, for 10 dogs, we need to purchase 15 bags of dog food.
Step 3: Substitute the number of bags into m(x) to find the amount of money needed.
Substituting b(x) = 15 into m(x), we have: m(15) = 3(15) + 1.
Evaluating this expression gives us m(15) = 45 + 1 = 46.
Therefore, when there are 10 dogs at the shelter, the manager needs to bring $46 for the dog food purchase.