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