A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor

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?

Let the cost of the soda be p. So the cost of a hot dog is 2p.

The total cost of hot dogs:
2hp

The total cost of sodas:
ps

The total cost of both equals d. So we set the total cost of hots dogs plus sodas equal to d:
2hp + ps = d

We want to know the cost of a soda (p). So we have a literal equation. We factor out p from the left side:
p(2h + s) = d

Divide each side of the equation by (2h + s)
p(2h + s)/(2h + s) = d/(2h + s)

Cancel the (2h + s) on the left side, we get:
p = d/(2h + s)