Natalie has $50 to spend at the amusement park. If admission costs $24, she spends $12.50 on food, and each game is $1.25 per play, write an equation that represents her total spending, y, and x as the number of games played. Then find how many games she can play before she runs out of money.
A. y = 50 – 1.25x ; she can play 40 games
B. y = 1.25x + 36.50 ; she can play 10 games*
C. y = 1.25x + 36.50 ; she can play 11 games
D. y = 12.50x + 50 ; she can play 4 games
To write an equation that represents Natalie's total spending, we need to consider the different expenses she incurs.
The cost of admission is $24, and she spends $12.50 on food. Each game costs $1.25. So the equation for her total spending, y, can be expressed as:
y = 24 + 12.50 + 1.25x
We add up the cost of admission ($24), the cost of food ($12.50), and the cost of games played ($1.25x).
Next, we need to find out how many games she can play before she runs out of money.
Natalie's total spending, y, cannot exceed the $50 she has to spend. Therefore, we need to solve the equation:
24 + 12.50 + 1.25x ≤ 50
Combine like terms:
37.50 + 1.25x ≤ 50
Subtract 37.50 from both sides:
1.25x ≤ 12.50
Divide both sides by 1.25:
x ≤ 10
So, Natalie can play a maximum of 10 games before she runs out of money.
Comparing the options, the correct answer is:
B. y = 1.25x + 36.50 ; she can play 10 games