Write System of Equations from Context

Question

Kiran is going to a carnival that has games and rides. Each game costs $1.50 and each ride costs $3. Kiran spent $18 altogether at the carnival and the number of games he played is 4 times the number of rides he went on. Write a system of equations that could be used to determine the number of games Kiran played and the number of rides Kiran went on. Define the variables that you use to write the system.

Answer 1

Let G= the number of games played Each Game costs $1.50

Let R=the number of rides taken Each Ride Costs $3

The total spent at the carnival is $18.

So the number of games x the cost per game + the number of rides x the cost for rides equals $18

G($1.50) + R($3) = $18

The Number of games played is 4 times the number of rides.

G=4R

So your system of equations is

G($1.50) + R($3) = $18

G=4R

You can solve this by substitution.

Replace G in the 1st equation

4R($1.50)+R($3)=$18

$6R+$3R=$18

R=2

G=4R so G= 8

Check.. 8($1.50)+2($3)= $18