Question

Joanie believes that you cannot use cross products to solve the proportion StartFraction 50 over 3 EndFraction = StartFraction 75 over x EndFraction for x. She says that if you multiply both sides of the equation by x, you get StartFraction 50 x over 3 EndFraction = 75. Then, if you multiply both sides of the equation by 3, you get 50 x = 75, which is a different equation than you would get if you cross multiplied. What mistake did Joanie make in her reasoning?
She assumed that the multiplication property of equality allows her to multiply both sides of the equation StartFraction 50 over 3 EndFraction = StartFraction 75 over x EndFraction by x.
She assumed that the multiplication property of equality allows her to multiply both sides of the equation StartFraction 50 x over 3 EndFraction = 75 by 3.
She assumed that 50 x = 75 is the equation that you get if you multiply both sides of the equation StartFraction 50 x over 3 EndFraction = 75 by 3.
She assumed that mc013-8.jpg is a different equation than you would get if you cross multiplied to solve the proportion StartFraction 50 over 3 EndFraction = StartFraction 75 over x EndFraction for x.

Answer 1

I'm assuming it's supposed to be written like this:
\(\LARGE\frac{50}{3}=\frac{75}{x}\)

Answer 2

Solving that we start off by cross multiplying,
\(\LARGE\frac{50}{3}=\frac{75}{x}\)

\(50*x=(75)*(3)\)

\(50x=225\)

Answer 3

Then dividing both sides using the fraction bars as division (fractions are division)

So we divide it by 50,
\(\LARGE\frac{50x}{50}=\frac{225}{50}\)

Answer 4

So. to find \(x\)
You will need to solve, \(\LARGE\frac{50x}{50}=\frac{225}{50}\)
You might be able to solve this already without work,
but what you do to do this is `cross multiply`, then `÷2500` to both sides.
Which would look like this,
\(\sf Cross\ multiplying:\)
\(50x*(50)=(225)*(50)\)
\(2500x=11250\)
\(\sf ÷2500,\ both\ sides\)
\(\LARGE\frac{2500x}{2500}=\frac{11250}{2500}\)
You didn't have to do this part but this should give you your answer.
\(\LARGE x=\frac{?}{?}\)

Answer 5

\(\LARGE\frac{2500x}{2500}=\frac{11250}{2500}\)
2500x/2500 would cancel right?

Answer 6

then wut is left is 11250/1500

Answer 7

which needs to be simplified

Answer 8

then it should give the overall answer ?

Answer 9

11250/1500=11250÷1500

Answer 10

11250÷1500=7.5