Question

Kyle is buying gifts for Megan's birthday and needs to stay in budget

Cake = half his money + 36.50
Decorations = half of what he had left + 36.50
Sweets = half of what he had left + 18.25

Now he is out of money, what did he start with?

Answer 1

Answer: Let's start by using algebra to represent the problem.

Let X be the amount of money that Kyle started with.

Then we can create the following equations:

• Cake = 0.5X + 36.50
• Decorations = 0.5(X - Cake) + 36.50
• Sweets = 0.5(X - Cake - Decorations) + 18.25

And we know that he's out of money, so:

• Cake + Decorations + Sweets = X
• We can use substitution to solve for X.

Substitute the first equation into the second equation to get:

• Decorations = 0.5(X - (0.5X + 36.50)) + 36.50
• Decorations = 0.25X + 9.25

Substitute the first two equations into the third equation to get:

• Sweets = 0.5(X - (0.5X + 36.50) - (0.25X + 9.25)) + 18.25
• Sweets = 0.25X + 4.75

Substitute all three equations into the fourth equation to get:

(0.5X + 36.50) + (0.25X + 9.25) + (0.25X + 4.75) = X

Simplify and solve for X:

• 1X + 50.50 = X
• 50.50 = 0.5X
• X = 101

Therefore, Kyle started with $101.