Question
For how many games is the total cost of bowling equal for the two bowling establishments ?
Hint:
1. Cost of gaming = Number of games played × price per game
2. Total cost = Cost of gaming + cost of shoes.
Let the number of games be x.
As per the given diagram, we observe that-
Cost of gaming for family bowling = $ 4
Cost of shoes for family bowling = $ 1
Cost of gaming for Knight owl bowling = $ 3.75
Cost of shoes for Knight owl bowling = $ 2
The correct answer is: For 4 games, the total cost of bowling will be equal for the two bowling establishments.
Step-by-step solution:-
Cost of gaming for Family bowling = Number of games played * cost per game
∴ Cost of gaming for Family bowling = x * 4
∴ Cost of gaming for Family bowling = 4x .................................................................. (Equation i)
Cost of gaming for Knight Owl Bowling = Number of games played * cost per game
∴ Cost of gaming for Knight Owl Bowling = x × 3.75
∴ Cost of gaming for Knight Owl Bowling = 3.75x ...................................................... (Equation ii)
Total cost of gaming through Family bowling = Cost of gaming + cost of shoes
∴ Total cost of gaming through Family bowling = 4x + 1 ............. (From Equation i & given information) ........... (Equation iii)
Total cost of gaming through Knight Owl bowling = Cost of gaming + cost of shoes
∴ Total cost of gaming through Knight Owl bowling = 3.75x + 2 ............. (From Equation ii & given information) ........... (Equation iv)
To find the value of x, we solve the equations representing cost of gaming in both the situations together-
4x + 1 = 3.75x + 2 .................................................... (From Equations iii & iv)
∴ 4x - 3.75x = 2 - 1 ...................................... (Taking all constants and variables on either sides of the equation)
∴ 0.25x = 1
∴ x = 1/0.25 ............................................. (Dividing both sides by 0.25)
∴ x = 4
Final Answer:-
∴ For 4 games, the total cost of bowling will be equal for the two bowling establishments.
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