Question

Joanie believes that you cannot use cross products to solve the proportion 50/3=75/x for x. She says that if you multiply both sides of the equation by x, you get 50x/3=75. Then, if you multiply both sides of the equation by 3, you get 50x=75, which is a different equation than you would get if you cross multiplied. What mistake did Joanie make in her reasoning?

Answer 1

Joanie made a mistake in her reasoning when 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. This assumption is incorrect because the multiplication property of equality states that if you multiply both sides of an equation by the same non-zero number, the resulting equation is still true. However, in this case, x is unknown and could potentially be zero. If x were zero, then multiplying both sides of the equation by x would result in an equation with undefined terms. Therefore, you cannot directly multiply both sides of the equation by x in this case.

Instead, to solve the proportion StartFraction 50 over 3 EndFraction = StartFraction 75 over x EndFraction for x, you can use cross products. Cross products involve multiplying the numerator of one fraction by the denominator of the other fraction. In this case, the cross products would be 50 * x and 3 * 75. Setting these cross products equal to each other gives you the equation 50x = 3 * 75.

To solve for x, you would divide both sides of the equation by 50 to isolate x. This would give you the equation x = (3 * 75) / 50. Simplifying this equation would give you the value of x.
Hope It Helps :)

Answer 2

In the equation 50/3=75/x
multiplying both sides by x we get:
50x/3=75
multiplying both sides by 3 we get
50x=225
this implies that the mistake that Joanie made was that she forgot to multiply 75 by 3.
thus
50x≠75.