Year 9 Maths- Simutaneous Equation

Question

The entry fee for a fun run is $10 for adults and $3 for children. A total of $3360 was collected
from the 420 competitors. Find the number of adults running and the number of children running.

Answer 1

You have two equations and two unknowns! Yessss!

 

Let A = # of Adult Tickets

Let C = # of Child Tickets

 

Equation 1: A+C = 420

 

Equation 2: 10A + 3C = 3360

 

Using substitution: C = 420 - A (from equation 1)

 

Plugging that value of C into equation 2, you get:

 

10A + 3 (420 - A) = 3360

 

10A + 1260 - 3A = 3360

 

7A = 3360 - 1260 = 2100

 

Thus A = 2100/7 = 300

 

And since C = 420 - 300 = 120

 

300 Adults and 120 Children ran the fun run!