Larry is taking orders for lunch. a roast beef sandwich costs $5 and a taco salad costs $7.50. he collects $127.50 from the 19 people who ordered. assuming everyone who ordered just ordered 1 item, how many people ordered taco salads? (3 points. 1 point for setting up a correct system of equation, 1 point for the work, 1 point for the correct solution.)

System of equations:

5r +7.50t = 127.50

r +t = 19

t = 13 . . . number of people who ordered taco salads

Step-by-step explanation:

One equation expresses the total bill: the number of each item ordered multiplied by its price, all item subtotals added to make the order total.

The other equation expresses the total number of orders: the sum of the orders of roast beef sandwich and the orders of taco salads.

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The solution can be found easily by substitution.

r = 19 -t

5(19 -t) +7.50t = 127.50

95 +2.50t = 127.50 . . . . . . simplify

2.50t = 32.50 . . . . . . . . . . subtract 95

t = 13 . . . . . . . . . . . . . . . . . . divide by 2.50

The number who ordered taco salads is 13.