Money Math-Trick Question

Kane has $50.00. He goes to the supermarket and buys football boots and then he buys a soccer ball, which is half the price of the football boots.He then spends half of what she has left on a belt, leaving him with $15.00.

How much did the soccer ball cost?

How much did the football boots cost?

I started it like this:

Let x= price of football boots

Let 1/2(x) = price of soccer ball

the combined cost of soccer ball and football boots = x + 1/2(x)

Amount spent on the football boots and soccer ball :

$50-(

**I am stuck**

The text gives a clue that the price of the belt = $15

(How did they arrive at the conclusion that the price of the belt equals $15?)

Anyone has any ideas as to how I can move on?

Thanks

Re: Money Math-Trick Question

let y be the amount of money after he buys both football and soccer boots.then the price of the belt is 1/y.after buying the belt he has $15.so the equation is:

y-y/2=$15

can you solve it from here?

Re: Money Math-Trick Question

Quote:

Originally Posted by

**KayPee** Kane has $50.00. He goes to the supermarket and buys football boots and then he buys a soccer ball, which is half the price of the football boots.He then spends half of what she has left on a belt, leaving him with $15.00.

How much did the soccer ball cost?

How much did the football boots cost?

I started it like this:

Let x= price of football boots

Let 1/2(x) = price of soccer ball

the combined cost of soccer ball and football boots = x + 1/2(x)

Amount spent on the football boots and soccer ball :

$50-(

**I am stuck**

The text gives a clue that the price of the belt = $15

(How did they arrive at the conclusion that the price of the belt equals $15?)

Anyone has any ideas as to how I can move on?

Thanks

Let x be the price of the boots

After buying the football and the football boots he is left with: $\displaystyle y = \left[50 - \left(x+ \dfrac{x}{2}\right)\right]$

He then spends half of this on the belt and is left with $15: $\displaystyle y - \dfrac{y}{2} = 15$

Of course we have an expression for y in x so sub that in:

$\displaystyle \left[50 - \left(x+ \dfrac{x}{2}\right)\right] - \dfrac{1}{2}\left[50 - \left(x+ \dfrac{x}{2}\right)\right] = 15$

And after simplification:

$\displaystyle \left(50 - \dfrac{3x}{2}\right) - \left(25 - \dfrac{3x}{4}\right) = 15$

Solve for x, which is the price of the boots

Re: Money Math-Trick Question

Quote:

Originally Posted by

**KayPee** Kane has $50.00. He goes to the supermarket and buys football boots and then he buys a soccer ball, which is half the price of the football boots.He then spends half of what **she** has left on a belt, leaving him with $15.00.

Well, you said this was a trick question! Who is "she" and how much money does she have?

Quote:

How much did the soccer ball cost?

How much did the football boots cost?

I started it like this:

Let x= price of football boots

Let 1/2(x) = price of soccer ball

the combined cost of soccer ball and football boots = x + 1/2(x)

Amount spent on the football boots and soccer ball :

$50-(

**I am stuck**

The text gives a clue that the price of the belt = $15

(How did they arrive at the conclusion that the price of the belt equals $15?)

Anyone has any ideas as to how I can move on?

Thanks

You were told that he spent "half of what [s]he has left on a belt" and then had $15 left. If you spend "half", you have "half" left.

That means that before buying the belt, he had $30. That means that the boots and ball cost 50- 30= $20. Taking x to be the cost of the boots, the ball cost x/2 so x+ x/2= 3x/2= 20.