SOLUTION: Anjali and joe improved their yards by planting daylilies and ivy. They bought their supplies from the same store. Anjali spent $233 on 13 daylilies and 14 pots of ivy. Joe spent $
Question 1103078: Anjali and joe improved their yards by planting daylilies and ivy. They bought their supplies from the same store. Anjali spent $233 on 13 daylilies and 14 pots of ivy. Joe spent $109 on 5 daylilies and 7 pots of ivy. find the cost of one daylily and the cost of one pot of ivy Found 2 solutions by addingup, ikleyn:Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website! 13d + 14i = 233
5d + 7i = 109 multiply all times -2 and add to above
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13d + 14i = 233
+
-10d - 14i = -218
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3d 0i = 15
3d = 15
d = 5 the daylilies are 5 each. Now let's solve for ivy:
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13(5) + 14i = 233
65 + 14i = 233
14i = 168
i = 12 the ivy are 12 per pot.
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In case you are wondering, you would get the same answer using the other equation to find i:
5d + 7i = 109
5(5) + 7i = 109
25 + 7i = 109
7i = 84
i = 84/7 = 12
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Happy learning!
From the condition, you have the system of 2 equations in 2 unknowns
13*d + 14*p = 233, (1) (Anjali' spending)
5*d + 7*p = 109. (2) (Joe' spending)
To solve the system, multiply equation (2) by 2 (both sides). The modified system is
13*d + 14*p = 233, (3)
10*d + 14*p = 218. (4)
Now subtract eq(4) from eq(3) (both sides). The terms "14*p" in both equations will cancel each other, and
you will get a single equation for only one unknown "d" (it is how the Elimination method works):
3d = 233 - 218 = 15 ====> d = = 5.
Thus you found that the pot of ivy costs $5.
Then from eq(2), 7p = 109 - 5*5 = 84 and d = = 12.
Answer. One daylily costs $12 and one pot of ivy costs $5.
