SOLUTION: Lance ́s sandwich shop sold 4 kinds of sandwiches yesterday. For every bologna sandwich 3 turkey sandwiches were sold. For every turkey sandwich sold 1.5 ham sandwiches were s

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Lance ́s sandwich shop sold 4 kinds of sandwiches yesterday. For every bologna sandwich 3 turkey sandwiches were sold. For every turkey sandwich sold 1.5 ham sandwiches were s      Log On


   



Question 1029418: Lance ́s sandwich shop sold 4 kinds of sandwiches yesterday. For every bologna sandwich 3 turkey sandwiches were sold. For every turkey sandwich sold 1.5 ham sandwiches were sold. 30 roast beef sandwiches were sold. If only whole sandwiches were sold and bologna sandwiches made up 10% of the total number of sandwiches sold, how many bologna sandwiches were sold?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of bologna sandwiches sold
Let +b+ = number of turkey sandwiches sold
Let +c+ = number of ham sandwiches sold
+30+ = number of roast beef sandwiches sold
-----------------------------------------
(1) +a%2Fb+=+1%2F3+
(2) +b%2Fc+=+2%2F3+
(3) +a+=+%281%2F10%29%2A%28+a+%2B+b+%2B+c+%2B+30+%29+
----------------------------
(3) +10a+=+a+%2B+b+%2B+c+%2B+30+
(3) +9a+-+b+-+c+=+30+
and
(1) +a+=+%281%2F3%29%2Ab+
and
(2) +c+=+%283%2F2%29%2Ab+
-------------------
By substitution:
(3) +9%2A%281%2F3%29%2Ab+-+b+-+%283%2F2%29%2Ab+=+30+
(3) +3b+-+b+-+%283%2F2%29_%2Ab+=+30+
(3) +b%2A%28+6%2F2+-+2%2F2+-+3%2F2+%29+=+30+
(3) +b%2A%28+1%2F2+%29+=+30+
(3) +b+=+60+
and
(1) +a+=+%281%2F3%29%2Ab+
(1) +a+=+%281%2F3%29%2A60+
(1) +a+=+20+
and
(2) +c+=+%283%2F2%29%2Ab+
(2) +c+=+%283%2F2%29%2A60+
(2) +c+=+90+
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20 bologna sandwiches were sold
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check answer:
(3) +a+=+%281%2F10%29%2A%28+a+%2B+b+%2B+c+%2B+30+%29+
(3) +a+=+%281%2F10%29%2A%28+20+%2B+60+%2B+90+%2B+30+%29+
(3) +a+=+200%2F10+
(3) +a+=+20+
OK