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Rick Ross owns a flower shop named Ricky Rosé. He ordered 200 flowers for Mother's Day. He ordered roses at $1.50 each, carnations at $5.75 each, and daisies at $2.60 each. He ordered mostly roses, and 20 fewer carnations than daisies. The total order came to $589.50. How many of each type of flower was ordered?

Respuesta :

Answer:

80 roses, 50 carnations and 70 daisies were ordered.

Step-by-step explanation:

From the information provided, you can write the following equations:

x+y+z=200 (1)

1.50x+5.75y+2.60z=589.50 (2)

z=y+20 (3)

First, you can replace (3) in (1) and (2):

x+y+y+20=200

x+2y=180

1.50x+5.75y+2.60(y+20)=589.50

1.50x+5.75y+2.60y+52=589.50

1.50x+8.35y=537.50

Now, you have 2 equations:

x+2y=180 (4)

1.50x+8.35y=537.50 (5)

You can solve for x in (4):

x=180-2y (6)

Then, you can replace (6) in (5) and solve for y:

1.50(180-2y)+8.35y=537.50

270-3y+8.35y=537.50

5.35y=267.50

y=267.50/5.35

y=50

You can replace the value of y in (6) to find x:

x=180-2(50)

x=180-100

x=80

Finally, you can replace the value of y in (3) to find z:

z=y+20

z=50+20

z=70

According to this, the answer is that 80 roses, 50 carnations and 70 daisies were ordered.

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