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8 orchid and 12 lily plants sell for $362.

12 orchid and 8 lily plants sell for $388.
How much for the lily plant?

8 orchid and 12 lily plants sell for $362. 12 orchid and 8 lily plants sell for $388. How-example-1

1 Answer

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Answer:

Orchids sell for $22 each and Lilies sell for $15.5 each.

Explanation:

Let O and L stand for the price for each Orchid and Lily plant, respectively.

We are told that 8O + 12L = $362

We also learn that 12O + 8L = $388

We have two unknowns (O and L) and two equations. By using substitution, we should be able to find answers for both O and L.

Rearrange one of the equations to solve for either O or L. Lets use the first equation and solve for O:

8O + 12L = $362

8O = $362 - 12L

O = ($362 - 12L)/8

Now use this definition of O in the second equation:

12O + 8L = $388

12($362 - 12L)/8 + 8L = $388 [for O = ($362 - 12L)/8]

($4344 - 144L)/8 + 8L = $388

$543 - 18L + 8L = $388

-10L = -$155

L = $15.5 Lily plants sell for $15.5 each

From 8O + 12L = $362 we can calculate O (Orchid)

8O + 12L = $362

8O + 12($15.5) = $362

8O + $186 = $362

8O = $176

O = $22 Orchids sell for $22 each

CHECK:

Do 8 Orchid and 12 Lily plants total $362?

8*($22) + 12*($15.5) = $362 ?

$176 + $186 = $362 ?

$362 = $462 YES

Do 12 Orchid and 8 Lilly plants sell for $388?

12*($22) + 8*($15.5) = $388 ?

($264) + ($124) = $388 ?

$388 = $388 YES

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