A snack cart sells lemonade for $2 and hot dogs for $5. The vendor sold 86 items today for a total of $330. Which equation is true?

a. (86 - h) (h) = 86

b. (86 - h) + h = 86

c. (86 - h) + h = 2 + 5

d.[2 (86 - h) ] (5h) = 330

Let h be the number of lemonade sold. If the vendor sold 86 items today and h of them are lemonade, then the rest are hot dogs, so he sold 86-h hot dogs.

When you add the number of sold lemonade and hot dogs, then you get 86 items in total:

h + (86-h) = 86.

This equation is exactly the same as equation

(86-h) + h=86.

Moreover,

1. if a snack cart sells lemonade for $2, then he gets $2h for h sold lemonade;

2. if a snack cart sells hot dogs for $5, then he gets $5 (86-h) for (86-h) sold hot dogs.

In total he gets $330, then

2h+5 (86-h) = 330.

Both these equations are true, but only first is among given options.

Answer: correct choice is B.

The equation in B is true.

We know this in two ways. Firstly, we know since it sold 86 items, that we have the amount of hot dogs (h) and then the amount of lemonade would be (86 - h), or how ever many is left over after the hot dogs.

The second way we can know is by looking at the equation algebraically.

(86 - h) + h = 86

86 - h + h = 86

86 = 86 (TRUE)