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A number is 5 more than 3 times another number. The sum of the two numbers is 33. As an equation, this is written [tex]x + 3x + 5 = 33[/tex], where [tex]x[/tex] represents the smaller number. Plug in the numbers from the set [tex]\{3, 5, 7, 9\}[/tex] to find the value of [tex]x[/tex].

The value of [tex]x[/tex] that holds true for the equation is [tex]\square[/tex]. So, the smaller number is [tex]\square[/tex] and the larger number is [tex]\square[/tex].



Answer :

GinnyAnswer
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].