Final answer:
To find the number of hotdogs and hamburgers sold at the barbecue sale, we can set up a system of equations using the given information. Solving this system of equations will give us the values of x and y, which represent the number of hotdogs and hamburgers sold, respectively. Therefore, 100 hotdogs and 450 hamburgers were sold at the barbecue sale.
Step-by-step explanation:
To find the number of hotdogs and burgers sold at the barbecue sale, we can set up a system of equations using the given information.
Let x be the number of hotdogs sold and y be the number of hamburgers sold.
We know that the total number of hotdogs and hamburgers sold is 550, so we have the equation x + y = 550.
We also know that the total amount of money raised is $3,150.00, so we can write another equation for the total cost of the hotdogs and hamburgers: 4.50x + 6.00y = 3,150.00.
Solving this system of equations will give us the values of x and y, which represent the number of hotdogs and hamburgers sold, respectively.
To solve the system, we can multiply the first equation by 4.50 to eliminate x:
4.50x + 4.50y = 2,475.00.
Then subtract this equation from the second equation:
(4.50x + 6.00y) - (4.50x + 4.50y) = 3,150.00 - 2,475.00
1.50y = 675.00
Dividing both sides of the equation by 1.50 gives us:
y = 450
Substituting this value back into the first equation, we can find x:
x + 450 = 550
x = 550 - 450
x = 100
Therefore, 100 hotdogs and 450 hamburgers were sold at the barbecue sale.