Connect with a knowledgeable community and get your questions answered on IDNLearn.com. Get the information you need quickly and accurately with our reliable and thorough Q&A platform.
Sagot :
Alright, let's solve this step-by-step.
1. Identify the variables:
- Let the smaller number be [tex]\( x \)[/tex].
- Let the other number be [tex]\( y \)[/tex].
2. Set up the equations based on the problem statement:
- According to the problem, one number is 9 more than twice another number. This relationship can be expressed as:
[tex]\[ y = 2x + 9 \][/tex]
- The sum of the numbers is 129. This can be written as:
[tex]\[ x + y = 129 \][/tex]
3. Substitute the expression for [tex]\( y \)[/tex] into the second equation:
- From the first equation, we know that [tex]\( y = 2x + 9 \)[/tex]. Substitute [tex]\( y \)[/tex] in the second equation:
[tex]\[ x + (2x + 9) = 129 \][/tex]
4. Combine like terms and simplify:
- Combine [tex]\( x \)[/tex] and [tex]\( 2x \)[/tex]:
[tex]\[ 3x + 9 = 129 \][/tex]
5. Isolate [tex]\( x \)[/tex] by subtracting 9 from both sides of the equation:
- Subtract 9 from both sides:
[tex]\[ 3x = 120 \][/tex]
6. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 3:
- Divide both sides by 3:
[tex]\[ x = \frac{120}{3} \][/tex]
[tex]\[ x = 40 \][/tex]
So, the smaller number is [tex]\( x = 40 \)[/tex].
1. Identify the variables:
- Let the smaller number be [tex]\( x \)[/tex].
- Let the other number be [tex]\( y \)[/tex].
2. Set up the equations based on the problem statement:
- According to the problem, one number is 9 more than twice another number. This relationship can be expressed as:
[tex]\[ y = 2x + 9 \][/tex]
- The sum of the numbers is 129. This can be written as:
[tex]\[ x + y = 129 \][/tex]
3. Substitute the expression for [tex]\( y \)[/tex] into the second equation:
- From the first equation, we know that [tex]\( y = 2x + 9 \)[/tex]. Substitute [tex]\( y \)[/tex] in the second equation:
[tex]\[ x + (2x + 9) = 129 \][/tex]
4. Combine like terms and simplify:
- Combine [tex]\( x \)[/tex] and [tex]\( 2x \)[/tex]:
[tex]\[ 3x + 9 = 129 \][/tex]
5. Isolate [tex]\( x \)[/tex] by subtracting 9 from both sides of the equation:
- Subtract 9 from both sides:
[tex]\[ 3x = 120 \][/tex]
6. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 3:
- Divide both sides by 3:
[tex]\[ x = \frac{120}{3} \][/tex]
[tex]\[ x = 40 \][/tex]
So, the smaller number is [tex]\( x = 40 \)[/tex].
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.