Question

A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost?

Answer 1

A soda costs $\frac{100d}{(s+2h)}$ cents

Step-by-step explanation:

A vendor sells h hot dogs and s sodas

• A hot dog costs twice as much as a soda
• The vendor takes in a total of d dollars

We need to find how many cents does a soda cost

Assume that the cost of a soda is x cents

∵ The cost of a hot dog is twice as a soda

- Twice means multiply by 2

∵ The cost of a soda = x cents

∴ The cost of a hot dog = 2x

∵ The total cost of h hot dog and s soda is $d

∵ 1 dollar = 100 cents

- Change the total cost to cents

∴ $d = d × 100 = 100d cents

∵ The vendor sells h hot dogs and s soda

∴ The total cost of h hot dog and s soda = s(x) + h(2x)

∴ The total cost of h hot dog and s soda = sx + 2hx

- Equate the total cost by 100 d

∴ sx + 2hx = 100d

- Take x as a common factor from the left hand side

∴ x(s + 2h) = 100d

- Divide both sides by (s + 2h)

∴ $x=\frac{100d}{(s+2h)}$

∵ x represents the cost of a soda in cents

∴ The cost of a soda is $\frac{100d}{(s+2h)}$ cents

A soda costs $\frac{100d}{(s+2h)}$ cents

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

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