Question

It costs $5 for an adult and $2 for a student to visit the national botanical gardens. Adults can be members of the botanical society and if you are a member, you can visit the gardens for free. A group of 30 adults and students visited the gardens. Five members of the group could go in for free and it cost the rest of the group $104 to go in. How many students were in the group? SIMULTANEOUS LINEAR EQUATIONS

Answer 1

Answer:

x = 7 (the number of students)

Step-by-step explanation:

let students = x , adults =y

Equation 1: the  total number of them

x+y=25  (25 because there are 5 for free)

Equation 2: the total price of them

2x+5y=104       (student cost 2$, adult cost 5$)

so we have two equations

x+y=25      (by multiply this equation by -2)

so it will be -2x-2y=-50

by adding 2 equations

-2x-2y=-50

2x+5y=104

0+3y = 54   divide both side by 3

y=18      (the number of adults)

by sub. in Equation (x+y=25)

x+18=25

x=25-18

x = 7 (the number of students)