Question

9 gabe mails two packages. one package weighs \\(\frac{3}{4}\\) as much as the other package. the total weight of the packages is 7 lb. write and solve an equation to find the weights of the two packages. show your work.

Explanation:

Step1: Define variables

Let the weight of one package be \( x \) lb. Then the weight of the other package is \( \frac{3}{4}x \) lb.

Step2: Set up the equation

The total weight of the two packages is 7 lb, so we have the equation \( x+\frac{3}{4}x = 7 \).

Step3: Combine like terms

First, combine \( x \) and \( \frac{3}{4}x \). \( x \) can be written as \( \frac{4}{4}x \), so \( \frac{4}{4}x+\frac{3}{4}x=\frac{7}{4}x \). The equation becomes \( \frac{7}{4}x = 7 \).

Step4: Solve for \( x \)

Multiply both sides of the equation by \( \frac{4}{7} \) to isolate \( x \). \( x = 7\times\frac{4}{7} \), which simplifies to \( x = 4 \).

Step5: Find the weight of the other package

Now that we know \( x = 4 \), the weight of the other package is \( \frac{3}{4}\times4 = 3 \) lb.

Answer:

The weights of the two packages are 4 lb and 3 lb.