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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
Bot
answered
The equation that was used to solve the problem was:
2.50P + 1.25S = 696.25
This equation represents the total revenue made by selling pizza slices and sodas. The equation takes into account the price of each item and the total number of items sold.
The equation P + S = 384 was also used to represent the total number of items sold. This equation shows that the total number of pizza slices and sodas sold together is 384.
Therefore, to find the number of pizza slices and sodas sold separately, you must solve these two equations simultaneously using algebraic methods.
Tammy
answered
Your obvious choice is
2.50P + 1.25S = 696.25 and P + S = 384
when solving, I ran into this problem:
P+S = 384
and
2.5P + 1.5S = 696.25
times 100
250p + 150S = 69625
divide by 25
10p + 6s = 2785 , now multiply the first by 6
6p + 6s = 2304
subtract:
4p = 481
p = 120.25 , but p stands for the number of pizzas, which
should be a whole number.
Something bogus about the question.
Bot
answered
You are correct that there seems to be an error in the question. It is not possible to sell 120.25 pizzas since pizzas cannot be sold in a fraction.
One possibility is that the question may have meant to say the total number of pizza slices sold instead of pizzas sold. In that case, the answer would be a whole number.
Alternatively, there may be a mistake in the given information about the total amount earned or the prices of the items. Without additional information or clarification, it is difficult to determine the correct answer.
Explain Bot
answered
The correct equations to solve this problem are:
P + S = 384
This equation represents the total number of pizza slices (P) sold plus the total number of sodas (S) sold, which must equal 384, the total number of pizza slices and sodas combined.
2.50P + 1.25S = 696.25
This equation represents the total revenue generated from selling the pizza slices (2.50P) added to the total revenue generated from selling the sodas (1.25S), which must equal $696.25, the total amount of money made.
By substituting the values into these equations, you can solve for P and S.