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6 balloons

Step-by-step explanation:

Clowns Are Fun equation is

y = 1.25x + 6  (1.25 per balloon plus the flat rate $6 delivery charge)

Singing Balloons equation

y = 1.95x + 2  (1.95 per balloon plus the flat rate $2 delivery charge)

We want to know know the value of x that makes Clowns are Fun less that Singing Balloons, so we have the inequality..

1.25x + 6 < 1.95x + 2      now solve for x

4 < 0.7x                

  5.7 < x          We can't have 0.7 of a balloon, so we round to 6.  

So when she orders 6 or more balloons, the cost of Clowns Are Fun will be cheaper that the cost of Singing Balloons

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation: