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
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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) (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.
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