A group of 42 people go to the zoo. The admission price is 6$ For adults and 3$ for kids. If the group spent 162$, how many adults and kids were in the group?

Answer: 12 adults, 30 kids

Step-by-step explanation:

Let x represent the number of adult and y represent the number of kids, then from the first statement;

x + y = 42 ... equation 1

For adults, the admission price is $6, the total cost for x adults will be 6x, Also, the admission price for kids is $3, this means that the total cost for y kids is 3y. The group spent $162 in all, this means that

6x + 3y = 162 ... equation 2

Solving the system of linear equation by substitution method, from equation 1, make x the subject of the formula, that is

x = 42 - y ... equation 3

substitute x = 42 - y into equation 2, we have

6 (42 - y) + 3y = 162

252 - 6y + 3y = 162

252 - 3y = 162

Add 3y to both sides of the equation, we have

252 = 162 + 3y

subtract 162 from both sides of the equation

252 - 162 = 3y

90 = 3y

divide through by 3

Therefore : y = 30

substitute y = 30 into equation 3, that is

x = 42 - y

x = 42 - 30

x = 12

Therefore : there are 12 adults and 30 kids