You are running a concession stand at a basketball game. You are selling pizza slices and sodas. Each pizza slice sells for $2.50 and each soda sells for $1.25. At the end of the night you made a total of $696.25. You sold a total of 384 pizza slices and sodas combined. You must report the number of pizza slices sold and the number of sodas sold. What equations did you use to solve this where P = the number of pizza slices sold and S = the number of sodas sold?
P + S = 696.25 and P + S = 384
2.50P + 1.25S = 696.25 and P + S = 384
2.50 + 1.25 = 696.25 and P + S = 384
2.50S + 1.25P = 384 and P + S = 696.25
The correct equations used to solve this problem are:
2.50P + 1.25S = 696.25 (Total revenue equation)
P + S = 384 (Total sales equation)
Explanation:
The first equation represents the total revenue generated from selling pizzas and sodas. The price of a pizza slice is $2.50 and the price of a soda is $1.25. To find the total revenue, we need to multiply the number of pizzas sold (P) by the price of each pizza slice ($2.50) and add it to the number of sodas sold (S) multiplied by the price of each soda ($1.25).
The second equation represents the total number of pizzas and sodas sold. We know that the total number of sales (384) is the sum of the number of pizzas sold (P) and the number of sodas sold (S).
Now we have two equations and two variables (P and S). We can solve the system of equations simultaneously to find the values of P and S.
Using substitution or elimination method, we can solve for one variable in terms of the other and substitute it into one of the equations to solve for the remaining variable.
For example, using substitution method:
P + S = 384 (Total sales equation) => S = 384 - P
Substitute S = 384 - P into the revenue equation:
2.50P + 1.25S = 696.25
2.50P + 1.25(384 - P) = 696.25
2.50P + 480 - 1.25P = 696.25
1.25P = 216.25
P = 173
So, 173 pizza slices were sold. To find the number of sodas sold, substitute P = 173 into the sales equation:
P + S = 384
173 + S = 384
S = 211
So, 211 sodas were sold.
Therefore, the number of pizza slices sold is 173 and the number of sodas sold is 211. And the correct equations used to solve this problem are 2.50P + 1.25S = 696.25 and P + S = 384.
Your answer is 384 I had this question yesterday
I apologize for the mistake in my previous answer. You are correct that the total number of pizza slices and sodas sold is given in the problem statement as 384. Thanks for bringing this to my attention.
The correct equations to solve this problem are:
2.50P + 1.25S = 696.25 (Total revenue equation)
P + S = 384 (Total sales equation)
Using substitution or elimination method, we can solve for the values of P and S. For example, using substitution method:
P + S = 384 (Total sales equation) => S = 384 - P
Substitute S = 384 - P into the revenue equation:
2.50P + 1.25S = 696.25
2.50P + 1.25(384 - P) = 696.25
2.50P + 480 - 1.25P = 696.25
1.25P = 216.25
P = 173
So 173 pizza slices were sold, and then we can find the number of sodas sold by substituting P = 173 into the sales equation:
P + S = 384
173 + S = 384
S = 211
Therefore, the number of pizza slices sold is 173 and the number of sodas sold is 211. I apologize again for any confusion caused by my previous answer.
The correct equations to solve this problem are:
P + S = 384 (equation 1) - This equation represents the total number of pizza slices (P) sold plus the total number of sodas (S) sold, which should equal 384 since that is the total number of pizza slices and sodas combined.
2.50P + 1.25S = 696.25 (equation 2) - This equation represents the total revenue made from selling pizza slices and sodas. The price of each pizza slice is $2.50 (2.50P) and the price of each soda is $1.25 (1.25S). When you multiply the price of each item by the number sold and add them together, it should equal $696.25, which is the total revenue.
Therefore, the correct set of equations to solve this problem is:
P + S = 384 (equation 1)
2.50P + 1.25S = 696.25 (equation 2)