Question: Four people placed orders at Olive Gardens for foodfor their parties.

Question

Question: Four people placed orders at Olive Gardens for foodfor their parties.

Andrew ordered two plates of ravioli, 1 plate of lasagna, 3orders of salad and breadsticks, and 4 pizzas. His total was$99.05.

Audrey ordered 2 orders of salad and breadsticks, 3 plates ofravioli, 1 pizza, and 2 plates of lasagna. Her total was$80.70.

Isaac ordered 2 pizzas, 3 orders of salad and breadsticks, 5plates of lasagna and 1 plate of ravioli. His total was$118.60.

Bella ordered 3 plates of lasagna, 3 pizzas, 4 plates of ravioliand 1 order of salad and breadsticks. Her total was smudged off herreceipt.

All together, the 4 people spent a total of $419.45 with no taxor tip. How much does each dish cost?

NEED HELP AND SHOW ALL WORK PLEASE! I WILLRATE HIGHLY IF YOU REALLY HELP! SHOW ALL WORK AND CORRECTANSWER!

Explanation / Answer

O.K. The first thing we need to do is to organize the data. It will help you to make a table. Here's what I got:              Ravioli   Lasagna   Salad+BS  Pizza   Cost Andrew     2           1               3           4         99.05 Audrey       3            2              2            1         80.7 Isaac          1            5              3            2         118.6 Bella           4            3               1             3        121.1* * I got the last cost by subtracting the total cost by therest of the costs (419.45 - 99.05 - 80.75 - 118.6 = 121.1) Thats the easy part the next part is a little moredifficult. O.K. we need to assign variables for each five of thesecatogories. Let: Ravioli = V Lasagna = W Salid and Breadsticks = X Pizza = Y Now we have four equations: 2V +   W + 3X + 4Y = 99.05 3V + 2W + 2X +   Y = 80.7 V + 5W + 3X + 2Y = 118.6 4V + 3W +   X + 3Y = 121.1 So we have four equations and four variables which isjust enough information to solve this problem. The next step is to take our system of equaitions and makethem a Matrix Here's our Matrix: [ 2 1 3 4 99.05 ] [ 3 2 2 1 80.7   ] [ 1 5 3 2 118.6 ] [ 4 3 1 3 121.1 ] Now row reduce it (This can be done on a graphingcalculator or by hand) and you will get: [ 1 0 0 0 9.95 ] [ 0 1 0 0 13.25] [ 0 0 1 0 6.3   ] [ 0 0 0 1 11.75] This tells us this W = 9.95 V = 13.25 X = 6.3 Y = 11.75 In other words: Each plate of ravioli costs $9.95 Each plate of lasagna costs $13.25 Each plate of salid and bread sticks costs $6.30 and Each plate of pizza costs $11.75 I hope this helps, The Math Geronimo

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