SOLUTION: Three salesman went to 400 households to sell a certain brand of rice cookers costing $60 each.15% of the households bought a rice cooker each from them.if the three salesman sold

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Question 213416: Three salesman went to 400 households to sell a certain brand of rice cookers costing $60 each.15% of the households bought a rice cooker each from them.if the three salesman sold ricecooker in the ratio 3:4:5, find the commission each salesman recieved if the commission is 4% of the total sales
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The number of households that bought rice cookers was
.15%2A400+=+60
Each household bought 1 rice cooker
Let a = the number sold by salesman A
Let b = the number sold by salesman B
Let c = the number sold the salesman C
(1) a+%2B+b+%2B+c+=+60
(2) a%2Fb+=+3%2F4
(3) b%2Fc+=+4%2F5
This is 3 equations with 3 unknowns, so it should be solvable
From (2)
a+=+%283%2F4%29%2Ab
From (3)
c+=+%285%2F4%29%2Ab
Now rewrite (1)
%283%2F4%29%2Ab+%2B+b+%2B+%285%2F4%29%2Ab+=+60
Multiply both sides by 4
3b+%2B+4b+%2B+5b+=+240
12b+=+240
b+=+20
and
a+=+%283%2F4%29%2Ab
a+=+%283%2F4%29%2A20
a+=+15
and
c+=+%285%2F4%29%2Ab
c+=+%285%2F4%29%2A20
c+=+25
The 3 salesmen charged $60 for each rice cooker
A's $ sales = 15%2A60+=+900
B's $ sales = 20%2A60+=+1200
C's $ sales = 25%2A60+=+1500
A's commision = .04%2A900+=+36
B's commision = .04%2A1200+=+48
C's commision = .04%2A1500+=+60
Hope I didn't misread the problem!