2 Algebra word problems, please help?

answers are GREATLY appreciated =]



1. The income (y0 for selling x tubs of toothpaste is modeled by the equation y=2.5x dollars. The production cost (y) for x tubes of toothpaste is modeled by the equation y=0.9x+3000 dollars.

-How many tubes of toothpaste must be sold for the income to equal the production cost?

-What is the income and production cost at the point when they are equal?

-The company makes a profit when their incomve is greater than their production cost. What is the least number of toothpast tubes the company can sell to make a profit?


2.
*define variables
A telephone company offers customers two payment plants for monthly service

Plan A costs $5 per month plus $0.10 per minute for calls.
Plan B costs $8 per month plus $0.07 per minute for calls

*How many minutes of calls would it take for Plan A and Plan B to cost the same?

thankyou so much!!

1a. To find when the income and production costs are equal, put the two equations equal to each other and solve for x

.09x + 3000 = 2.5x

x = 1875

1b. To find what the income and production costs are when they are equal, you need to plug in 1875 to each equation

.09 =(1875) + 3000 = $4,687.50

2.5(1875) = $4,687.50

1c. At 1875 tubes the income and cost equal each other and no profit is made. In order to make a profit you would need to sell 1876.


2.
5 + .10x = 8 + .07x

5 + .03x = 8

.03x = 3

.03x/.03 = 3/.03

x = 100

2.

5+.10x=8+.07
.03x=3
x=100

1.

quantity times price= Revenue
Revenue-C=Profit

Number 1.

* 2.5x = 0.9x + 3000
1.6x = 3000
1.6x/1.6 = 3000/1.6
1, 875 tubes of toothpaste.

I'm sorry, but I'm not sure about the other 2 on question 1.

Number 2.

5 + .10x = 8 + .07x
5 + .03x = 8
.03x = 3
.03x/.03 = 3/.03
x = 100
100 minutes.

for number two i got 10.

1) 2.5x = 0.9x+3000

2.5x(-0.9x) = 0.9x(-0.9x)+3000

1.6x = 3000

1.6x / 1.6 = 3000 / 1.6

x = 1875

- 1875 tubes of toothpaste
- 2.5 * 1875 = $4687.5 equal cost
- Must sell at least 1876 tubes for a profit


2) 5 + .10x = 8 + .07x

5(-5) + .10x = 8(-5) + .07x

.10x (-.07x) = 3 + .07x(-.07x)

.03x = 3

.03x / .03 = 3 / .03

x = 100 Minutes