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:

Ben is 20 years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was 3 times as old as Daniel. How old is Daniel now?

Ben is \(20\) years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was \(3\) times as old as Daniel.\newlineHow old is Daniel now?

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve a system of equations using any method: word problemsright chevron icon

Full solution

Q. Ben is \(20\) years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was \(3\) times as old as Daniel.\newlineHow old is Daniel now?
  1. Equation 11: Ben's age: Let's denote Ben's current age as BB and Daniel's current age as DD. According to the problem, Ben is 2020 years older than Daniel, which gives us the first equation:\newlineB=D+20B = D + 20
  2. Equation 22: Three years ago: The problem states that three years ago, Ben was 33 times as old as Daniel. We need to account for their ages three years ago, so we subtract 33 from their current ages:\newlineB−3=3(D−3)B - 3 = 3(D - 3)
  3. System of equations: Now we have a system of two equations:\newline11) B=D+20B = D + 20\newline22) B−3=3(D−3)B - 3 = 3(D - 3)\newlineWe can substitute the value of BB from the first equation into the second equation to solve for DD.\newline(D+20)−3=3(D−3)(D + 20) - 3 = 3(D - 3)
  4. Substituting BB into equation 22: Simplify the equation: D+17=3D−9D + 17 = 3D - 9
  5. Simplifying the equation: Now, we will solve for DD by moving all terms involving DD to one side and constants to the other side:\newline17+9=3D−D17 + 9 = 3D - D\newline26=2D26 = 2D
  6. Solving for D: Divide both sides by 22 to find the value of D:\newline262=D\frac{26}{2} = D\newlineD=13D = 13
  7. Checking the solution: Now that we have Daniel's current age, we can check if the information given in the problem is consistent with our solution. Three years ago, Daniel was 13−3=1013 - 3 = 10 years old. According to the problem, Ben was three times as old as Daniel three years ago. So, Ben's age three years ago should be 3×10=303 \times 10 = 30 years old. Since Ben is 2020 years older than Daniel, his current age should be 13+20=3313 + 20 = 33 years old. Checking for Ben's age three years ago: 33−3=3033 - 3 = 30, which is consistent with the problem.

More problems from Solve a system of equations using any method: word problems

Question
Solve using substitution. 5x−2y=−7 5x - 2y = -7 x=−5 x = -5 (_,_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Is (1,1)(1,1) a solution to this system of equations? \newline4x+10y=144x + 10y = 14\newlinex+6y=7x + 6y = 7\newlineChoices:\newline(A) yes \newline(B) no
Get tutor helpright-arrow

Posted 5 months ago

Question
Which describes the system of equations below?\newliney=–3x+9y = –3x + 9 \newliney=–3x+9y = –3x + 9 \newlineChoices:\newline(A) consistent and independent\text{(A) consistent and independent} \newline(B) consistent and dependent\text{(B) consistent and dependent} \newline(C) inconsistent\text{(C) inconsistent}
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve using elimination. \newline7x−8y=−17 7x - 8y = -17 \newline −7x+3y=2 -7x + 3y = 2 \newline (____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve. \newlinex=−2 x = -2 \newline−2x+2y=−8 -2x + 2y = -8 \newline(____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 9 months ago

Question
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineAt a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases 33 hot dog meals and 33 hamburger meals, paying a total of $36\$36. Mr. Hogan buys 11 hot dog meal and 33 hamburger meals, spending $26\$26 in all. How much do the meals cost?\newlineHot dog meals cost $\$_______ each, and hamburger meals cost $\$________ each.
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve the system of equations by substitution.\newline−3x−y−3z=−11-3x - y - 3z = -11\newlinez=5z = 5\newlinex−y+3z=19x - y + 3z = 19\newline(____.____,____)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve the system of equations by elimination.\newlinex−3y−2z=10 x - 3y - 2z = 10 \newline3x+2y+2z=14 3x + 2y + 2z = 14 \newline2x−3y−2z=16 2x - 3y - 2z = 16 \newline(_,_,_)(\_,\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve the system of equations.\newliney=x2+36x+3 y = x^2 + 36x + 3 \newliney=22x−37 y = 22x - 37 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_)(\_,\_)\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve the system of equations.\newliney=−x−24 y = -x - 24 \newlinex2+y2=488 x^2 + y^2 = 488 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) \newline(_,_) (\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

View all (92)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant