SOLUTION: Julio and Molly each improved their yards by planting hostas and geraniums. They bought their supplies from the same store. Julio spent $160 on 13 hostas and 1 geranium. Molly spe

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Julio and Molly each improved their yards by planting hostas and geraniums. They bought their supplies from the same store. Julio spent $160 on 13 hostas and 1 geranium. Molly spe      Log On


   

Question 1075725: Julio and Molly each improved their yards by planting hostas and geraniums. They bought their
supplies from the same store. Julio spent $160 on 13 hostas and 1 geranium. Molly spent $180
on 12 hostas and 9 geraniums. Find the cost of one hosta and the cost of one geranium.
I can't seem to figure this out at all. Please help?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the cost of 1 hosta
Let +b+ = the cost of 1 geranium
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Julio's equation:
(1) +13a+%2B+1%2Ab+=+160+
Molly's equation:
(2) +12a+%2B+9b+=+180+
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Divide both sides of (2) by +3+
(2) +4a+%2B+3b+=+60+
Multiply both sides of (1) by +3+
and subtract (2) from (1)
-----------------------------------
(1) +39a+%2B+3b+=+480+
(2) +-4a+-+3b+=+-60+
--------------------------
+35a+=+420+
+a+=+12+
and
(2) +4a+%2B+3b+=+60+
(2) +4%2A12+%2B+3b+=+60+
(2) +3b+=+60+-+48+
(2) +3b+=+12+
(2) +b+=+4+
-------------------------
The cost of 1 hosta is $12
The cost of 1 geranium is $4
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check answer:
(1) +13a+%2B+1%2Ab+=+160+
(1) +13%2A12+%2B+1%2A4+=+160+
(1) +156+%2B+4+=+160+
(1) +160+=+160+
OK You can check (2)