SOLUTION: Hi stock B cost twice as much as stock A , but the profit on B was only 3/4 as much as on A when both were sold. what was the cost of each stock if; a)the total cost was $3000

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Question 1119629: Hi
stock B cost twice as much as stock A , but the profit on B was only 3/4 as much as on A when both were sold.
what was the cost of each stock if;
a)the total cost was $3000.00
b)the total selling price $2,700 resulted in an average 20% profit on the cost.
thanks
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the cost of stock A
+2c+ = the cost of stock B
Let +p+ = the profit from selling stock A
+%283%2F4%29%2Ap+ = the profit from selling stock B
--------------------------------------------
(a)
+c+%2B+2c+=+3000+
+3c+=+3000+
+c+=+1000+
and
+2c+=+2000+
Stock A cost $1,000
Stock B cost $ 2,000
------------------------
(b)
The total selling price for A and B was both costs
plus both profits, so
(1) +c+%2B+p+%2B+2c+%2B+%283%2F4%29%2Ap+=+27000+
The average of the profits is
+%28+p+%2B+%283%2F4%29%2Ap+%29+%2F+2+
and this is equal to
(2) +%28+p+%2B+%283%2F4%29%2Ap+%29+%2F+2+=+.2%2A%28+c+%2B+2c+%29+
----------------------
(1) +3c+%2B+%287%2F4%29%2Ap+=+27000+
(1) +12c+%2B+7p+=+108000+
and
(2) +%28+%28+7%2F4%29%2Ap+%29+%2F+2++=+.2%2A3c+
(2) +%28+7%2F4+%29%2Ap+=+1.2c+
(2) +7p+=+4.8c+
(2) +p+=+%2848%2F70%29%2Ac+
(2) +p+=+%2824%2F35%29%2Ac+
Plug this into (1)
(1) +12c+%2B+7%2A%28+24%2F35+%29%2Ac+=+108000+
(1) +12c+%2B+%2824%2F5%29%2Ac+=+108000+
(1) +60c+%2B+24c+=+540000+
(1) +84c+=+540000+
(1) +c+=+6428.57%0D%0Aand%0D%0A%7B%7B%7B+2c+=+12857.14+
------------------
A cost $6,428.57
B cost $12,857.14
------------------
check:
(1) +3c+%2B+%287%2F4%29%2Ap+=+27000+
(1) +3%2A6428.57+%2B+%287%2F4%29%2Ap+=+27000+
(1) +19285.71+%2B+%287%2F4%29%2Ap+=+27000+
(1) +%287%2F4%29%2Ap+=+7714.29+
(1) +p+=+%284%2F7%29%2A7714.29+
(1) +p+=+4408.17+
and
(2) +%287%2F4%29%2Ap+=+1.2c+
(2) +7714.29+=+1.2c+
(2) +c+=+6428.58+
close enough
--------------------------
Definitely get a 2nd opinion on this if you can

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
stock B cost twice as much as stock A , but the profit on B was only 3/4 as much as on A when both were sold.
what was the cost of each stock if;
a)the total cost was $3000.00
b)the total selling price $2,700 resulted in an average 20% profit on the cost.
thanks
a)  Let cost of stock A be A

    Then cost of stock B = 2A

    We then get: A + 2A = 3,000____3A = 3,000

    A, or 

    



b)  2,700 = 1.2C, since selling price ($2,700) was 20% more than the combined cost 

    C, or cost of both = matrix%281%2C3%2C+%222%2C700%22%2F1.2%2C+%22=%22%2C+%22%242%2C250%22%29%29

    Let cost of stock A be A

    Then cost of stock B = 2A

    We then get: A + 2A = 2,250____3A = 2,250

    A, or 

    

I don't see any use for this statement: "but the profit on B was only 3/4 as much as on A when both were sold," unless I misunderstood or misread the problem.