Hotdogs and corndogs were sold at last night’s football game. Use the information below to write equations to help you determine how many corndogs were sold.
The number of hotdogs sold was three fewer than twice the number of corndogs sold. Write an equation relating the number of hotdogs and corndogs. Let h represent the number of hotdogs and c represent the number of corndogs. A hotdog costs $3 and a corndog costs $1.50. If $201 was collected, write an equation to represent this information. How many corndogs were sold? Show how you calculated your answer.

If we set up our equation using the unknown number of hot dogs and corn dogs with their individual prices attached to them, we can set the sum of them equal to $201. We know that a hot dog costs $3, so we can represent hot dogs monetarily by attaching the cost of a single hot dog to the h. For example, if a hot dog costs $3, and we represent the expression as 3h, with h being the number of hot dogs sold, if we sell 4 hot dogs at $3 apiece, we make $12. If we sell 6 hot dogs we will make $18. The same goes for the corn dogs. We don't know how many corn dogs or hot dogs we sold, but we do know that the sales of both made $201. So our expression for that is

3h + 1.50c = 201

That's great, but we have too many unknowns, and that's a problem. So let's look back up to where we are told that the number of hot dogs is 3 less than 2 times the number of corn dogs. "3 less than" is -3 algebraically. "Twice the number" is 2times and the words "is" and "was" represent the = sign. So putting those words into an algebraic equation looks like this:

h = 2c - 3

That says "the number of hot dogs was twice the number of corn dogs less 3". Now that we have an expression for hot dogs we can sub it into our money equation in place of h:

3h + 1.5c = 201 becomes 3(2c - 3) + 1.5c = 201

Now we have an equation with only c's in it.

Distribute through the parenthesis to get

6c - 9 + 1.5c = 201

Simplify to 7.5c = 210

Now divide by 7.5 to get that c = 28.

Now that we know that, we go back with that number and sub it in for c in

h = 2c - 3 --> h = 2(28) - 3 gives us that the number of hot dogs sold was 53

adioabiola adioabiola · Answer 2 · 2021-12-02T12:34:54+01:00

The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53

let

h = number of hotdogs

c = number of corndogs.

cost of hotdog = $3

corn dog = $1.50

The equation:

3h + 1.50c = 201 (1)

h = 2c - 3 (2)

substitute (2) into (1)

3(2c - 3) + 1.50c = 201

6c - 9 + 1.50c = 201

7.50c - 9 = 201

7.50c = 201 + 9

7.50c = 210

c = 210/7.50

c = 28

Therefore,

h = 2c - 3

= 2(28) - 3

= 56 - 3

= 53