Motel

Three different dinners A, B, and C are served in the motel. Three 20 members went to a motel. Group 1 ordered dinner A 20 members, and their average dinner price in the group was CZK 200. From Group 2, they ordered dinner A: 10 persons, B 10 dinners, and their average dinner price for the group was 240 CZK. From Group 3, they ordered five persons A dinners, B 5 dinners, a C 10 dinners, and their average dinner price was CZK 270. Calculate the price of dinner A, B, and C.

A =  200
B =  280
C =  300

Step-by-step explanation:

20·A=20·200
10·A +10·B = 20·240
5·A+5·B+10·C = 20·270

20A = 4000
10A+10B = 4800
5A+5B+10C = 5400

Row 2 - 10/20 · Row 1 → Row 2
20A = 4000
10B = 2800
5A+5B+10C = 5400

Row 3 - 5/20 · Row 1 → Row 3
20A = 4000
10B = 2800
5B+10C = 4400

Row 3 - 5/10 · Row 2 → Row 3
20A = 4000
10B = 2800
10C = 3000

C = 3000/10 = 300
B = 2800/10 = 280
A = 4000/20 = 200

A = 200
B = 280
C = 300

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