A group of friends went to an amusement park and played 3 games of mini-golf and 7 arcade games for $45.50. Another group of friends played 4 games of mini-golf and 11 arcade games for $63.80.
Solve the system of equations. What is the closest answer to the cost of a game of mini-golf?
Let the cost of a mini-golf game =
.
Let the cost of an arcade game =
.
Let's set up a system of equations based on the information given:
3x + 7y = 45.50
4x + 11y = 63.80
Where x represents the cost of a mini-golf game and y represents the cost of an arcade game.
To solve the system of equations, we can use the elimination method:
Step 1: Multiply the first equation by 4 and the second equation by 3 to make the coefficients of x equal:
12x + 28y = 182 (4(3x + 7y = 45.50))
12x + 33y = 191.40 (3(4x + 11y = 63.80))
Step 2: Subtract the first equation from the second equation:
12x + 33y - (12x + 28y) = 191.40 - 182
5y = 9.40
y = 1.88
Step 3: Substitute the value of y into one of the original equations to solve for x:
3x + 7(1.88) = 45.50
3x + 13.16 = 45.50
3x = 32.34
x = 10.78
Therefore, the cost of a game of mini-golf is approximately $10.78.