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

GIVEN :

The equation is $\frac{50}{3}=\frac{75}{x}$ for x.

a) She assumed that the multiplication property of equality allows her to multiply both sides of the given equation  $\frac{50}{3}=\frac{75}{x}$ by x.

b) She assumed that the multiplication property of equality allows her to multiply both sides of the equation $\frac{50}{3}=\frac{75}{3}$ .

c) She assumed that 50x = 75 is the equation that you get if you multiply both sides of the equation $\frac{50}{3}=\frac{75}{3}$.

d) She assumed that mc013-8.jpg is a different equation than you would get if you cross multiplied to solve the proportion Start Fraction 50 over 3 End Fraction= Start Fraction 75 over x End Fraction for x.

TO FIND :

The mistake of Joanie make in her reasoning

SOLUTION :

Given that Joanie believes that we cannot use cross products to solve the proportion $\frac{50}{3}=\frac{75}{x}$ for x.

She says that if we multiply both the sides of the equation by x, you get $\frac{50x}{3}=75$Then multiply both the sides of the equation by 3, we get 50 x = 75.

The mistake she had done is " She assumed that 50 x = 75 is the equation that you get if you multiply both sides of the equation Start Fraction 50 x over 3 End Fraction = 75 by 3." is correct.

ie., option c) is correct.

The corrected steps are

$\frac{50}{3}=\frac{75}{x}$

Multiply both the sides of the above equation by x, you get

$\frac{50x}{3}=75$.

Then multiply both the sides of the equation by 3, you get

$50x = 75\times 3$.