https://file.aiquickdraw.com/mathbot/file/1727406629901tlbs1i0q.jpg

To solve the problem stated in the image, let's define the weights and set up an equation based on the information given:

1. The weight of the first package is \(1 \frac{1}{2}\) pounds.
2. The weight of the second package is \(3 \frac{3}{4}\) pounds.
3. The weight of the third package is \(4 \frac{1}{4}\) pounds.
4. The weight of the fourth package is unknown.

The sum of the weights of the first two packages is equal to the sum of the weights of the third package and the unknown weight. Therefore, the equation is:

\[
1 \frac{1}{2} + 3 \frac{3}{4} = 4 \frac{1}{4} + x
\]

Converting mixed numbers to improper fractions:

\[
\frac{3}{2} + \frac{15}{4} = \frac{17}{4} + x
\]

To simplify, first find a common denominator for the fractions on the left side:

\[
\frac{3 \times 2}{2 \times 2} + \frac{15}{4} = \frac{6}{4} + \frac{15}{4} = \frac{21}{4}
\]

Now, substitute back into the equation:

\[
\frac{21}{4} = \frac{17}{4} + x
\]

Solving for \(x\):

\[
x = \frac{21}{4} - \frac{17}{4} = \frac{4}{4} = 1
\]

Therefore, the weight of the unknown package is \(1\) pound.

Would you like further details on any part of this calculation or have another question? Here are some potential follow-ups:

1. How can we convert mixed numbers to improper fractions?
2. What is the process for finding a common denominator?
3. How can equations be used to solve word problems in real-life scenarios?
4. Can you explain more about why the weights of the packages are expressed in fractions?
5. What other mathematical operations can be useful in solving similar problems?

**Tip:** Always make sure to convert all terms to a common format (like improper fractions) when solving equations involving mixed numbers to simplify calculations.

Two packages that weigh 1 1/2 pounds and 3 3/4 pounds have the same total weight as a 4 1/4 pound package plus another package of unknown weight. How much does the other package weigh?

Learn how to solve a word problem involving fractions where two packages weighing 1 1/2 pounds and 3 3/4 pounds have the same weight as a 4 1/4 pound package and an unknown weight. The step-by-step solution converts mixed numbers to improper fractions and solves for the unknown weight.

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