Question

Chelsea brought $21.50 to the state fair. She bought a burger, a souvenir, and a pass. The burger was 1/3 as much as the souvenir, and the souvenir cost 1/2 of the pass. Chelsea had $4.00 left over after buying these items. What was the cost of each item?

Answer 1

Answer: Let's start by setting up some equations based on the given information:

The cost of the burger is 1/3 of the cost of the souvenir:

burger = (1/3) * souvenir

The cost of the souvenir is 1/2 of the cost of the pass:

souvenir = (1/2) * pass

Chelsea had $4.00 left over after buying these items:

burger + souvenir + pass + 4.00 = 21.50

Now we can use these equations to solve for the cost of each item.

Substituting equation 2 into equation 1, we get:

burger = (1/3) * ((1/2) * pass)

burger = (1/6) * pass

Substituting this expression for burger into equation 3, we get:

(1/6) * pass + (1/2) * pass + pass + 4.00 = 21.50

Combining like terms, we get:

(11/6) * pass = 17.50

Solving for pass, we get:

pass = (6/11) * 17.50

pass = $9.55

Using equation 2, we can find the cost of the souvenir:

souvenir = (1/2) * pass

souvenir = (1/2) * 9.55

souvenir = $4.78

Finally, we can use equation 1 to find the cost of the burger:

burger = (1/3) * souvenir

burger = (1/3) * 4.78

burger = $1.59

So, the cost of the burger was $1.59, the cost of the souvenir was $4.78, and the cost of the pass was $9.55.

Explanation: