SOLUTION: Your company reached it sales goals for the year so you decide to buy dinner for your 45 employees. You find a restaurant that gives you a good deal on chicken dinners at $9 each,

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Your company reached it sales goals for the year so you decide to buy dinner for your 45 employees. You find a restaurant that gives you a good deal on chicken dinners at $9 each,       Log On


   



Question 1042468: Your company reached it sales goals for the year so you decide to buy dinner for your 45 employees. You find a restaurant that gives you a good deal on chicken dinners at $9 each, salmon dinners at $12 each and steak dinners at $15 each. The number of chicken dinners you order is half the sum of salmon and steak dinners. If the total coast of all the meals is $525, how many of each type of dinner do you buy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You need a total of 45 dinners
Let +a+ = number of chicken dinners ordered
Let +b+ = number of salmon dinners ordered
Let +c+ = number of steak dinners ordered
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(1) +a+=+%281%2F2%29%2A%28+b+%2B+c+%29+
(2) +a+%2B+b+%2B+c+=+45+
(3) +9a+%2B+12b+%2B+15c+=+525+
----------------------------
(1) +2a+=+b+%2B+c+
(1) +c+=+2a+-+b+
Substitute (1) into (2)
(2) +a+%2B+b+%2B+2a+-+b+=+45+
(2) +3a++=+45+
(2) +a+=+15+
----------------------------
(1) +c+=+2a+-+b+
(1) +c+=+2%2A15+-+b+
(1) +c+=+30+-+b+
Substitute (1) into (3)
(3) +9a+%2B+12b+%2B+15c+=+525+
(3) +9%2A15+%2B+12b+%2B+15%2A%28+30+-+b+%29+=+525+
(3) +135+%2B+12b+%2B+450+-+15b+=+525+
(3) +-3b+=+525+-+585+
(3) +3b+=+60+
(3) +b+=+20+
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(1) +c+=+2a+-+b+
(1) +c+=+2%2A15+-+20+
(1) +c+=+30+-+20+
(1) +c+=+10+
-------------------
15 chicken dinners were ordered
20 salmon dinners were ordered
10 steak dinners were ordered
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check:
(1) +a+=+%281%2F2%29%2A%28+b+%2B+c+%29+
(1) +15+=+%281%2F2%29%2A%28+20+%2B+10+%29+
(1) +15+=+30%2F2+
(1) +15+=+15+
and
(2) +a+%2B+b+%2B+c+=+45+
(2) +15+%2B+20+%2B+10+=+45+
(2) +45+=+45+
and
(3) +9a+%2B+12b+%2B+15c+=+525+
(3) +9%2A15+%2B+12%2A20+%2B+15%2A10+=+525+
(3) +135+%2B+240+%2B+150+=+525+
(3) +525+=+525+
OK