Question

Mrs travis wants to have the clown deliver balloons to her secretary's office. Clowns R Fun charges $1.25 per balloon and $6 for delivery. Singing Balloons charges $1.95 per gallon and $2 for delivery. What is the minimum number of balloons Mrs. Travis needs to purchase in order for Clowns R Fun to have a lower price than Singing Balloons?

Answer 1

The correct answer is:

6 balloons.

Explanation:

Let x represent the number of balloons purchased.

We will call the function for Clowns R Fun c(x):

c(x) = 1.25x+6

We will call the function for Singing Balloons s(x):

s(x) = 1.95x+2

We want the amount for Clowns R Fun, c(x) to be less:

c(x) < s(x)

1.25x+6 < 1.95x+2

Subtract 1.25x from each side:

1.25x+6-1.25x < 1.95x+2-1.25x

6 < 0.7x+2

Subtract 2 from each side:

6-2 < 0.7x+2-2

4 < 0.7x

Divide each side by 0.7:

4/0.7 < 0.7x/0.7

5.7 < x

x > 5.7

She must buy more than 5.7 balloons; the next integer up is 6. She must buy 6 or more balloons.

Answer 2

Given:
Clowns R fun = 1.25 per balloon + 6 for delivery
Singing Balloons = 1.95 per balloon + 2 for deliver

1.25x + 6 = 1.95x + 2
1.25x - 1.95x = 2 - 6
-0.7x = -4
x = -4 / - 0.7
x = 5.71 or 6 balloons

Clowns R Fun = 1.25*6 + 6 = 7.5 + 6 = 13.5
Singing Balloons = 1.95*6 + 2 = 11.7 + 2 = 13.7  
If x is 6 = ALMOST THE SAME

Clowns R Fun = 1.25*5 + 6  = 6.25 + 6 = 12.25
Singing Balloons = 1.95*5 + 2 = 9.75 + 2 = 11.75
If x is 5 = Singing Balloons is cheaper

Clowns R Fun = 1.25*7 + 6 = 8.75 + 6 = 14.75
singing Balloons = 1.95*7 + 2 = 13.65 + 2 = 15.65 
If x is 7 = Clowns R Fun is cheaper

Mrs. Travis needs to order a minimum of 7 balloons in order for Clowns R Fun to have a lower price than Singing Balloons.