Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The sum of 33 consecutive integers is 5151. Which integers are they?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Consecutive integer problemsright chevron icon

Full solution

Q. The sum of 33 consecutive integers is 5151. Which integers are they?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_
  1. Define Integers: Let xx be the first integer. The three consecutive integers can be represented as xx, x+1x+1, and x+2x+2.
  2. Set Up Equation: Set up the equation to represent the sum of the three consecutive integers equal to 5151: x+(x+1)+(x+2)=51x + (x+1) + (x+2) = 51.
  3. Simplify Equation: Simplify the equation: x+x+1+x+2=51x + x + 1 + x + 2 = 51 becomes 3x+3=513x + 3 = 51.
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation: 3x+3−3=51−33x + 3 - 3 = 51 - 3 which simplifies to 3x=483x = 48.
  5. Divide to Solve: Divide both sides of the equation by 33 to solve for xx: 3x3=483\frac{3x}{3} = \frac{48}{3} which simplifies to x=16x = 16.
  6. Find Consecutive Integers: Now that we have the value of xx, we can find the three consecutive integers: x=16x = 16, x+1=16+1x+1 = 16+1, and x+2=16+2x+2 = 16+2. Therefore, the integers are 1616, 1717, and 1818.

More problems from Consecutive integer problems

Question
Solve for x. \newline(34)x=12(\frac{3}{4})x= 12 \newlinex=x = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for x. \newline−59x=15-\frac{5}{9}x= 15 \newlinex=x = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
How many solutions does the following equation have?\newline5x+8−7x=−4x+15x+8-7x=-4x+1\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline−2z+10+7z=16z+7-2z+10+7z=16z+7\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline7(y−8)=7y+427(y-8)=7y+42\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline−9(x+6)=−9x+108-9(x+6)=-9x+108\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline−6(x+7)=−4x−2-6(x+7)=-4x-2\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline−4x−7+10x=−7+6x-4x-7+10x=-7+6x\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline−17(y−2)=−17y+64-17(y-2)=-17y+64\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline9z−6+7z=16z−69z-6+7z=16z-6\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

View all (44)