Question

You are running a concession stand at a baseball game.

You are selling pizza slices and sodas.

Each pizza slice sells for $3.50 and each soda sells for $1.50.

At the end of the night, you made a total of $800.

You sold a total of 344 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?



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1 point
3.50S+1.50P=344 and P+S+800
3.50+1.50=800 and P+S=344
3.50P+1.50S=800 and P+S=344
P+S=800 and P+S=344
Mrs. Pope determined that the system of equations below has one solution.

The first line goes through the points (1, 2) and (2, 4)

The second line goes through the points (5, 15) and (10, 25)

Is she correct?

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1 point
No, the system has no solutions because the lines are parallel
No, the system has two solutions because the lines are parallel
Yes, the system has one solution which is (5, 15)
Yes, the system has one solution which is (1, 2)

Answer 1

1) Equations (with P = pizza slices, S = sodas):
3.50P + 1.50S = 800
P + S = 344
(That matches the choice "3.50P+1.50S=800 and P+S=344".)

Solve for counts:
P + S = 344 -> S = 344 − P
3.50P + 1.50(344 − P) = 800
3.50P + 516 − 1.50P = 800
2.00P = 284 -> P = 142 pizzas, S = 344 − 142 = 202 sodas.

2) Mrs. Pope’s system:
Slope of line through (1,2) and (2,4) = (4−2)/(2−1) = 2 (equation y = 2x).
Slope of line through (5,15) and (10,25) = (25−15)/(10−5) = 2 (equation y = 2x + 5).
Both slopes are 2 but different intercepts, so the lines are parallel and distinct — no solutions.
(Choice: "No, the system has no solutions because the lines are parallel.")