SOLUTION: daniel and kayla each improved their yards by planting daylilies and shrubs. they bought their supplies from the same store. daniel spent $156 on 8 daylilies and 14 shrubs. kayla s
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Question 1109271: daniel and kayla each improved their yards by planting daylilies and shrubs. they bought their supplies from the same store. daniel spent $156 on 8 daylilies and 14 shrubs. kayla spent $162 on 14 daylilies and 6 shrubs. what is the cost of one daylily and the cost of one shrub?
From the condition, you have the system of 2 equations in 2 unknowns
8*d + 14*s = 156, (1) (Daniel' spending)
14*d + 6*s = 162. (2) (Kayla' spending)
To solve the system, multiply equation (1) by 7 (both sides). multiply equation (2) by 4 (both sides). The modified system is
56*d + 98*s = 1092, (3)
56*d + 24*s = 648. (4)
Now subtract eq(4) from eq(3) (both sides). The terms "56*d" in both equations will cancel each other, and
you will get a single equation for only one unknown "s" (it is how the Elimination method works):
74s = 1092 - 648 = 444 ====> s = = 6.
Thus you found that one shrub costs $6.
Then from eq(1), 8d = 156 - 14*6 = 72 and d = = 9.
Answer. One daylily costs $9 and one shrub costs $6.
Solved. // On the way, you learned on how the Elimination method works.
