Aflorist has 54 white roses, 72 red roses, and 108 pink roses. if he makes the greatest number possible of identical bouquets using all the roses, how many red roses will be in each bouquet?

Find the greatest common factor of each flower:

White roses  = 54 = 1, 2 , 3, 6, 9,  18, 27, 54

Red roses = 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Pink roses = 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The common factors of all three are: 1, 2, 3, 6, 9, 18.

The greatest common factor is 18, so he can make 18 bouquets.

Divide the total red roses by 18:

72 / 18 = 4

There will be 4 red roses in each bouquet.

439400

step-by-step explanation:

130^2 = 16900

16900*26 = 439400

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!