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The cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20
<em><u>Solution:</u></em>
Let "a" be the cost of each ribeye steak dinners
Let "b" be the cost of each grilled salmon dinners
<em><u>A waitress sold 11 ribeye steak dinners and 12 grilled salmon dinners, totaling $560.63 on a particular day</u></em>
Thus we frame a equation as:
11 x cost of each ribeye steak dinners + 12 x cost of each grilled salmon dinners = 560.63
11a + 12b = 560.63 -------- eqn 1
<em><u>Another day she sold 16 ribeye steak dinners and 6 grilled salmon dinners, totaling $584.46</u></em>
Thus we frame a equation as:
16 x cost of each ribeye steak dinners + 6 x cost of each grilled salmon dinners = 584.46
16a + 6b = 584.46 ------------ eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Multiply eqn 2 by 2</u></em>
32a + 12b = 1168.92 ------- eqn 3
<em><u>Subtract eqn 1 from eqn 3</u></em>
32a + 12b = 1168.92
11a + 12b = 560.63
( - ) ----------------
21a = 1168.92 - 560.63
21a = 608.29
Divide both sides by 21
<em><u>Substitute a = 29 in eqn 1</u></em>
11(29) + 12b = 560.63
319 + 12b = 560.63
12b = 560.63 - 319
12b = 214.63
Divide both sides by 12
Thus cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20