Question 840647: The school's prom committee ordered 200 flowers to sell on Valentine's Day. The carnations cost $1.50 each, the pink roses cost $2.60 each and the long-stemmed red roses cost $5.75 each. Twenty more pink roses were ordered than red roses. The total order was $589.50. How many of each flower was ordered?
Answer by MPoaps(1)   (Show Source):
You can put this solution on YOUR website! Hi there, we can solve this problem by using substitution, elimination or matrices. I am going to use substitution. We have 3 unknown variables therefor we need 3 equation.
x=Carnations
y=Pink Roses
z=Red Roses(long stemmed)
Equations:
1. 1.50x + 2.60y + 5.75z =589.50
2. x + y + z =200
3. y= z + 20
Step1: We will substitute y because we have the formula rearranged as y=z+20
1.50x + 2.60(z+20) + 5.75z=589.50
1.50x + 2.60z + 52 + 5.75z= 589.50
1.50x+ 8.35z=537.50
Then we substitute for y in our 2nd formula
x +(z+20)+ z=200
x + 2z=180 therefore x= 180-2z
Then we substitute x into our formula's
#1. 1.50x + 8.35z=537.50
1.50(180-2z)+ 8.35z =537.50
270-3z + 8.35z=537.50
5.35z=267.5
---- ----
5.35 5.35
z=50
#2. x + 2z= 180
x + 2(50)= 180
x + 100= 180
x= 80
#3. y=z+20
y= 50+20
y= 70
We can now verify our answers by plugging them back into our original formula of 1.50x + 2.60y + 5.75z = 589.50
So 1.50(80)+2.60(70)+5.75(50)=589.50
120+182+287.50=589.50
And there we have it!:)
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