SOLUTION: A merchant mixes 4 lb of cinnamon tea with 1 lb of spice tea to create a mixture that costs $12 per pound. When the merchant mixes 1 lb of the cinnamon tea with 4 lb of the spice t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A merchant mixes 4 lb of cinnamon tea with 1 lb of spice tea to create a mixture that costs $12 per pound. When the merchant mixes 1 lb of the cinnamon tea with 4 lb of the spice t      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 927545: A merchant mixes 4 lb of cinnamon tea with 1 lb of spice tea to create a mixture that costs $12 per pound. When the merchant mixes 1 lb of the cinnamon tea with 4 lb of the spice tea, the mixture costs $15 per pound. Is the cost per pound of the cinnamon tea less than, equal to, or greater than the cost of the spice tea?
Please help me solve this thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = $ / pound of cinnamon tea
Let +b+ = $ / pound of spice tea
-----------------------------------
(1) +%28+4a+%2B+1%2Ab+%29+%2F+%28+4+%2B+1+%29+=+12+
(2) +%28+1%2Aa+%2B+4b+%29+%2F+%28+1+%2B+4+%29+=+15+
----------------------------------
(1) +%28+4a+%2B+b+%29+%2F+5+=+12+
(2) +%28+1%2Aa+%2B+4b+%29+%2F+5+=+15+
---------------------------
(1) +4a+%2B+b+=+60+
(2) +a+%2B+4b+=+75+
---------------------
Multiply both sides of (1) by +4+
and subtract (2) from (1)
(1) +16a+%2B+4b+=+240+
(2) +-a+-+4b+=+-75+
----------------------
+15a+=+165+
+a+=+11+
and
(2) +a+%2B+4b+=+75+
(2) +11+%2B+4b+=+75+
(2) +4b+=+64+
(2) +b+=+16+
----------------
The cost / pound of the cinnamon
tea is less than the spice tea