Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Jason plans to attend the Clark County Fair and is trying to decide what would be a better deal. He can pay $40 for unlimited rides, or he can pay $13 for admission plus $3 per ride. If Jason goes on a certain number of rides, the two options wind up costing him the same amount. What is that cost? How many rides is that?
for x rides, you want
40 = 13 + 3x
Now just solve for x
$40 = $13 + $3r
Subtract 13 from both sides, then divide them by 3 to find how many rides. The same amount = $40.
To set up a system of equations for this situation, we can let:
- x be the number of rides Jason goes on
- C be the cost in dollars
For the first option, where he pays $40 for unlimited rides, the cost can be represented as:
Cost of Option 1: C₁ = $40
For the second option, where he pays $13 for admission plus $3 per ride, the cost can be represented as:
Cost of Option 2: C₂ = $13 + $3x
Since the two options wind up costing him the same amount, we can set up an equation to represent this:
C₁ = C₂
$40 = $13 + $3x
Now, we can solve the equation using the substitution method.
Step 1: Substitute C₂ from the equation C₂ = $13 + $3x into C₁ = C₂.
$40 = $13 + $3x
Step 2: Simplify the equation.
$40 - $13 = $3x
$27 = $3x
Step 3: Divide both sides of the equation by $3 to solve for x.
$27/$3 = x
9 = x
So, Jason will spend $27 with both options when he goes on 9 rides.
Therefore, the cost of that situation would be $27 and the number of rides would be 9.