Answer:
28
Step-by-step explanation:
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
