SOLUTION: A company had 20 inch and 30 inch televisions is the ratio 4:7. 100 20 inch TVs were sold and 550 30 inch TVs were sold. Their ratio is now 1:1. How many TVs did the company s

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A company had 20 inch and 30 inch televisions is the ratio 4:7. 100 20 inch TVs were sold and 550 30 inch TVs were sold. Their ratio is now 1:1. How many TVs did the company s      Log On


   



Question 1084634: A company had 20 inch and 30 inch televisions is the ratio 4:7.
100 20 inch TVs were sold and 550 30 inch TVs were sold.
Their ratio is now 1:1.
How many TVs did the company start with

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the number of 20 inch televisions they had to start with.
let y = the number of 30 inch televisions they had to start with.

the ratio of 20 inch televisions to 30 inch televisions was 4/7.

x/y = 4/7

they sold 100 twenty inch televisions and 550 thirty inch televisions.

the ratio of 20 inch televisions to 30 inch televisions is now 1/1.

(x-100) / (y - 550) = 1/1

multiply both sides of the first equation by 7y to get:

7x = 4y

subtract 4y from both sides of the equation to get 7x - 4y = 0

multiply both sides of the second equation by (y - 550) to get:

(x - 100) = (y - 550)

remove parentheses to get:

x - 100 = y - 550

add 100 to both sides of this equation and subtract y from both sides of this equation to get:

x - y = -450

you have 2 equations that need to be solved simultaneously.

they are:

7x - 4y = 0

x - y = -450

leave the first equation as is and multiply both sides of the second equation by 4 to get:

7x - 4y = 0
4x - 4y = -1800

subtract the second equation from the first to get:

3x = 1800

solve for x to get:

x = 600

your original ratio is x/y = 4/7

when x = 600, this ratio becomes 600/y = 4/7

cross multiply to get 4y = 4200

solve for y to get y = 4200/4 = 1050

you have x = 600 and y = 1050

x/y = 600/1050 = 4/7

(x-100) / (y - 550) = (600 - 100) / (1050 - 550) = 500 / 500 = 1/1

these agree with the problem statements which confirms the solution is correct.

the solution is:

number of 20 inch televisions was originally 600 and number of 30 inch televisions was 1050.