purchased 12 cheeseburgers and 8 hot dogs which cost $33. On the way out of the park after the hike, the troop purchased 20 cheeseburgers and 10 hot dogs for $50. Find the price of a cheeseburger

Answer 1

We will set this up as a system of two equations in two variables. The unknowns here are the prices for each food item, so we can let "c" = cost of each cheeseburger and we can let "d" = cost of each hotdog. Both equations we write will involve adding the total amounts for each individual food item and setting the sum equal to the amount spent in all.

For the trip in to the park, the equation will be 12c + 8d = 33. For the trip out of the park, the equation will be 20c + 10d = 50. We could solve this system either by elimination or by substitution. If we go by way of substitution, it would be best to take the 2nd equation and divide everything by 10 to make the numbers smaller and to give us a variable we can easily isolate. So if we do this, the 2nd equation becomes 2c + d = 5.

Now if we isolate the "d" in this equation, it becomes d = 5 - 2c, and this expression for "d" will now be substituted into the other equation to replace the "d". So the other equation will now look like this:

12c + 8(5 - 2c) = 33. Eliminating our parentheses, we have 12c + 40 - 16c = 33, and if we combine like terms, we have -4c + 40 = 33. This then becomes -4c = -7, and dividing both sides by -4, we have c = 1.75, the cost of each cheeseburger.

Inserting this value for c into either of our original equations ( I'll use the second equation), we have 20(1.75) + 10d = 50. Solving this equation, we have 35 + 10d = 50 → 10d = 15 →d = 1.50, the cost of each hotdog.

Now we need to check both of these values in both of the original equations, just to make sure that they work, and they do, so we're looking at $1.75 for each burger and $1.50 for each hotdog.