https://file.aiquickdraw.com/mathbot/file/17267740494377j1735xd.jpg

The problem in the image states:

1. The sum of two numbers is 73. The second number is five less than half of the first number. Find the two numbers.

### Let’s break this down into equations:

Let the first number be \( x \), and the second number be \( y \).

1. The sum of the two numbers is 73:
   \[
   x + y = 73
   \]
   
2. The second number is five less than half of the first number:
   \[
   y = \frac{x}{2} - 5
   \]

### Now, substitute the second equation into the first:

\[
x + \left( \frac{x}{2} - 5 \right) = 73
\]

Simplify this equation:

\[
x + \frac{x}{2} - 5 = 73
\]

Add 5 to both sides:

\[
x + \frac{x}{2} = 78
\]

Multiply the whole equation by 2 to eliminate the fraction:

\[
2x + x = 156
\]

Combine the terms:

\[
3x = 156
\]

Solve for \( x \):

\[
x = \frac{156}{3} = 52
\]

Now that we know \( x = 52 \), substitute it into the second equation to find \( y \):

\[
y = \frac{52}{2} - 5 = 26 - 5 = 21
\]

### Therefore, the two numbers are 52 and 21.

Let me know if you need further details or explanations! Here are five related questions:

1. What if the sum of the two numbers was a different value, like 80?
2. How would the solution change if the second number were 5 more than half the first?
3. Can this problem be solved using a graphing method?
4. How would you represent this as a system of equations?
5. What are some other methods to solve this type of word problem?

**Tip**: When working with word problems, always define variables clearly and write out equations step-by-step to avoid confusion.

The sum of two numbers is 73. The second number is five less than half of the first number. Find the two numbers.

Learn how to solve the system of equations where the sum of two numbers is 73 and the second number is five less than half of the first. This algebraic problem focuses on solving linear equations using the substitution method. Suitable for Grades 8-10 students.

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