SOLUTION: The camera has 10.1 million pixels. The product of the pixels across the screen times the pixels up the screen gives the number of pixels the camera has. The ratio of pixels across

Algebra ->  Rectangles -> SOLUTION: The camera has 10.1 million pixels. The product of the pixels across the screen times the pixels up the screen gives the number of pixels the camera has. The ratio of pixels across      Log On


   

Question 564756: The camera has 10.1 million pixels. The product of the pixels across the screen times the pixels up the screen gives the number of pixels the camera has. The ratio of pixels across the screen to pixels up the screen is 4 : 3. How many pixels does this camera have across the screen? Explain what you are calculating as you solve the problem.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the ratio of horizontal pixels to vertical pixels is 4:3.
let x = the number of horizontal pixels.
let y = the number of vertical pixels.
the ratio of x to y is 4 to 3 which can be shown as:
x/y = 4/3
cross multiply to get:
3x = 4y
solve for y to get:
y = 3x/4
the total number of pixels is 10.1 million.
since the total number of pixels is the number of horizontal pixels times the number of vertical pixels, then your equation would be:
x * y = 10.1
since y = 3x/4, you can substitute for y in this equation to get:
x * 3x/4 = 10.1
simplify this equation to get:
3x^2/4 = 10.1
multiply both sides of this equation by 4 to get:
3x^2 = 40.4
divide both sides of this equation by 3 to get:
x^2 = 13.46666667
take the square root of both sides of this equation to get:
x = 3.669695719
since x * y = 10.1, substitute for x in this equation to get:
3.669695719 * y = 10.1
divide both sides of this equation by 3.669695719 to get:
y = 2.752271789
this suggest that:
the number of horizontal pixels across the screen is 3.669695719 million.
the number of vertical pixels across the screen is 2.752271789.
since the ratio of horizontal pixels to vertical pixels is 4/3, then that ratio should also be equal to 3.669695719 / 2.752271789.
your equation to see if that's true would be:
4/3 = 3.669695719 / 2.752271789.
you would cross multiply to get:
4 * 2.752271789 = 3 * 3.669695719
you would simplify that to get:
11.00908716 = 11.00908716 which suggest that the ratios are the same which means you probably have the right numbers of horizontal pixels and vertical pixels.
you would test that out by multiplying them together to get:
3.669695719 * 2.752271789 = 10.1.
all the numbers check out so that's your answer.