Danny brought $43.00 to the state fair. He bought a burger, a souvenir, and a pass. The burger was 1/4 as much as the souvenir, and the souvenir cost 2/3 the cost of the pass. Danny had $4.50 left over after buying these items. What was the cost of each item?

Here we have , Danny brought $43.00 to the state fair. He bought a burger, a souvenir, and a pass. The burger was 1/4 as much as the souvenir, and the souvenir cost 2/3 the cost of the pass. Danny had $4.50 left over after buying these items. We need to find What was the cost of each item . Let's find out:

Let value of pass is x ! So , the souvenir cost 2/3 the cost of the pass i.e.

⇒ [tex]\frac{2x}{3}[/tex]

Now , The burger was 1/4 as much as the souvenir i.e.

⇒ [tex]\frac{2x}{3}(\frac{1}{4} )[/tex]

⇒ [tex]\frac{x}{6}[/tex]

Total Cost = $43 , According to question we have following conditions :

⇒ [tex]\frac{x}{6} +\frac{2x}{3} +x+4.5=43[/tex]

⇒ [tex]\frac{x}{6} +\frac{4x}{6} +x=38.5[/tex]

⇒ [tex]\frac{5x}{6} +x=38.5[/tex]

⇒ [tex]\frac{11x}{6}=38.5[/tex]

⇒ [tex]x=38.5(\frac{6}{11} )[/tex]

⇒ [tex]x=21[/tex]

Therefore , Cost each item is : Pass = $21 , Souvenir = 2x/3 = $14 , Burger = x/6 =$3.5 .

astha8579 astha8579 · Answer 2 · 2022-04-26T07:37:19+02:00

The cost of each item that Danny bought in this case are: Pass of the fair was of $21, the cost of souvenir was $14 and the cost of burger was $3.5

How to form mathematical expression from the given description?

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Given that:

Total money Danny had in the state fair = $43
He bought a burger, a souvenir, and a pass
burger was 1/4 as much as the souvenir
souvenir cost 2/3 the cost of the pass
Amount remaining after buying all these things = $4.5

The cost of burger is expressed in terms of cost of souvenir and of souvenir in terms of the cost for pass.

So, let we take:
Cost of pass = x dollars,

Then, cost of souvenir = 2/3 of x = 2x/3 dollars

And the cost of burger = 1/4 of cost of souvenir = 1/4 (2x/3) = [tex]\dfrac{2x}{12} = \dfrac{x}{6}[/tex] dollars.

Also, we have:

Total initial amount = Amount spent + Amount remaining

or

43 = Cost of all those 3 items + 4.5

[tex]43 = x + \dfrac{2x}{3} + \dfrac{x}{6} + 4.5\\43 = \dfrac{6x}{6} + \dfrac{4x}{6} + \dfrac{x}{6} + 4.5\\\\43 = \dfrac{11x}{6} + 4.5\\\\\text{Subtracting 4.5 from both the sides}\\\\43-4.5 = \dfrac{1x}{6}\\\\\\dfrac{11x}{6} = 38.5\\\\\text{Multiplying 6/11 on both the sides}\\\\x = \dfrac{6 \times 38.5}{11} = 21[/tex]

Thus, the cost of pass was $21

Now, we get:

Cost of souvenir = 2x/3 = [tex]\dfrac{2(21)}{3} = 2\times7 = 14[/tex] dollars,

and cost of burger = [tex]\dfrac{x}{6} = \dfrac{21}{6} = 3.5[/tex] dollars.

Thus, the cost of each item that Danny bought in this case are: Pass of the fair was of $21, the cost of souvenir was $14 and the cost of burger was $3.5

Learn more about forming equations here:

https://brainly.com/question/11938672