Answer:
She ordered 80 carnations, 50 roses, and 70 daisies.
Step-by-step explanation:
Let x = number of carnations, y = number of roses, and z = number of daisies. This problem gives us three equations.
First, remember that we multiply the price of each flower by the number bought then add up the subtotals, that gives the total amount paid.
Therefore,
1.50x + 5.75y + 2.60z = 589.50
Second, the sum of the numbers purchased is the total bought. Therefore,
x + y + z = 200
Finally, there are 20 fewer roses than daisies. Therefore,
y = z - 20
If you substitute z - 20 in for y in the first two equations, you can rewrite them so they only have x and z.
1.50x + 5.75(z - 20) + 2.60z = 589.50
1.50x + 5.75z - 115 + 2.60z = 589.50
1.50x + 8.35z = 704.50
x + (z - 20) + z = 200
x + 2z - 20 = 200
x + 2z = 220
If you solve the rewrite second equation for x, you get x = 220 - 2z. Therefore, you can substitute 220 - 2z in for x in the rewritten first equation, and then solve for z.
1.50 (220 - 2z) + 8.35z = 704.50
330 - 3z + 8.35z = 704.50
330 + 5.35z = 704.50
5.35z = 374.50
z = 70
If you have z = 70, then x = 220 - 2(70) = 80 and y = 70 - 20 = 50.
She ordered 80 carnations, 50 roses, and 70 daisies.
*HOPE THIS HELPED!!! :D)
