Let's solve the problem step by step:
1. Understanding the problem:
- We have two numbers. Let's call the smaller number [tex]\( x \)[/tex].
- The larger number is 5 more than 3 times the smaller number, which can be written as [tex]\( 3x + 5 \)[/tex].
- The sum of these two numbers is 33. Therefore, we can write the equation:
[tex]\[ x + (3x + 5) = 33 \][/tex]
2. Solving the equation:
- Simplify the equation:
[tex]\[
x + 3x + 5 = 33
\][/tex]
[tex]\[
4x + 5 = 33
\][/tex]
- Subtract 5 from both sides of the equation:
[tex]\[
4x = 28
\][/tex]
- Divide both sides by 4:
[tex]\[
x = 7
\][/tex]
3. Verify the solution:
- The smaller number is [tex]\( x = 7 \)[/tex].
- Calculate the larger number using [tex]\( x \)[/tex]:
[tex]\[
3x + 5 = 3(7) + 5 = 21 + 5 = 26
\][/tex]
- Check the sum of the two numbers:
[tex]\[
7 + 26 = 33
\][/tex]
- This confirms that our solution is correct.
4. Determining the values:
- The value of [tex]\( x \)[/tex] that holds true for the equation is 7.
- Therefore, the smaller number is 7.
- The larger number is 26.
So, we fill in the blanks:
The value of [tex]\( x \)[/tex] that holds true for the equation is [tex]\( 7 \)[/tex]. So, the smaller number is [tex]\( 7 \)[/tex] and the larger number is [tex]\( 26 \)[/tex].
