Question

1. billy’s restaurant ordered 200 flowers for mother’s day. they ordered carnations at $1.50 each, roses at $5.75 each and daisies at $2.60 each. they ordered mostly carnations and 20 fewer roses than daisies. the total order came to $589.50. how many of each type of flower was ordered?

Explanation:

Step1: Define Variables

Let \( c \) be the number of carnations, \( r \) be the number of roses, and \( d \) be the number of daisies.
We know the following:

1. \( c + r + d = 200 \) (total number of flowers)
2. \( r = d - 20 \) (20 fewer roses than daisies)
3. \( 1.50c + 5.75r + 2.60d = 589.50 \) (total cost)

Step2: Substitute \( r \) in terms of \( d \) into the first equation

From \( c + r + d = 200 \) and \( r = d - 20 \), we get:
\( c+(d - 20)+d = 200 \)
Simplify: \( c + 2d-20=200 \)
So, \( c=220 - 2d \)

Step3: Substitute \( c \) and \( r \) into the cost equation

Substitute \( c = 220 - 2d \) and \( r = d - 20 \) into \( 1.50c + 5.75r + 2.60d = 589.50 \):
\( 1.50(220 - 2d)+5.75(d - 20)+2.60d = 589.50 \)
Expand: \( 330-3d + 5.75d-115 + 2.60d=589.50 \)
Combine like terms: \( ( - 3d+5.75d + 2.60d)+(330 - 115)=589.50 \)
\( 5.35d+215 = 589.50 \)

Step4: Solve for \( d \)

Subtract 215 from both sides: \( 5.35d=589.50 - 215=374.50 \)
Divide both sides by 5.35: \( d=\frac{374.50}{5.35} = 70 \)

Step5: Solve for \( r \)

Since \( r = d - 20 \), substitute \( d = 70 \):
\( r=70 - 20 = 50 \)

Step6: Solve for \( c \)

Since \( c=220 - 2d \), substitute \( d = 70 \):
\( c=220-2\times70=220 - 140 = 80 \)

Answer:

Number of carnations: 80, Number of roses: 50, Number of daisies: 70