write an equality and solve

Question

the zoo charges an admission price of $85 for the first 112 members of a group and $6 for each additional member of the group. what is the largest froup that can go to the zoo and spend less than $155 on admission

Answer 1

Let's let n be the number of people in a group.

 

So the price for a group would be 85 + (n-112) * 6.

 

That's a fixed rate of 85, plus 6 dollars for any additional person over the first 112 people.  That's why it's (n-112).

 

If you want the total cost to be less than $155, set this expression to be less than 155 and solve:

 

85 + (n-112) * 6 < 155

 

Simplify

85 + 6n - 672 < 1556n - 587 < 155

 

Add 587 to both sides:

6n < 742

 

Divide both sides by 6:

n < 123 2/3

 

So any group with less than 123 2/3 people would be OK.  Since you can't have 2/3 of a person, it means that 123 is the largest group that would cost less than $155.