SOLUTION: Solving Problems Using Linear Systems 1. Leanne works at a greenhouse. She needs to plant a total of 32 bulbs. Two types of bulbs are available. She is asked to plant three times

Question 185695: Solving Problems Using Linear Systems
1. Leanne works at a greenhouse. She needs to plant a total of 32 bulbs. Two types of bulbs are available. She is asked to plant three times as many crocus bulbs as tulip bulbs. How many of each should she plant?
(The answer is: 24 crocus bulbs and 8 tulip bulbs, but i dont know how to solve it?)
Can you pleaseeeeeeeeeeeeee help me with this problem thank you very much!!!!
Found 2 solutions by nerdybill, stanbon:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
1. Leanne works at a greenhouse. She needs to plant a total of 32 bulbs. Two types of bulbs are available. She is asked to plant three times as many crocus bulbs as tulip bulbs. How many of each should she plant?
.
Let x = number of crocus bulbs
and y = number of tulip bulbs
.
Because we have two unknowns, we'll need to find two equations.
.
From: "She needs to plant a total of 32 bulbs." we get equation 1:
x + y = 32
.
From: "She is asked to plant three times as many crocus bulbs as tulip bulbs." we get equation 2:
x = 3y
.
Our "system of equations" is:
x + y = 32
x = 3y
.
Take our definition of 'x' in equation 2 and substitute it into equation 1:
x + y = 32
(3y) + y = 32
4y = 32
y = 8 (tulip bulbs)
.
Now, plug our definition of 'y' above into equation 1 and solve for x:
x + y = 32
x + 8 = 32
x = 32-8
x = 24 (crocus bulbs)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. Leanne works at a greenhouse. She needs to plant a total of 32 bulbs. Two types of bulbs are available. She is asked to plant three times as many crocus bulbs as tulip bulbs. How many of each should she plant?
-------------------
Equations:
Quantity: c + t = 32
Quantity: c = 3t
-----------------------------
Rearrange:
c + t = 32
c -3t = 0
---------------------
Subtract the 2nd equation from the 1st to solve for "t":
4t = 32
t = 8 (# of tulips)
-----------
Since c = 3t, c = 24 (# of crocus)
=======================================
Cheers,
Stan H.

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