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:

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineBobby has been planting young trees in his garden. The maple tree that is 1414 inches tall is growing 22 inches per month, whereas the oak tree that is 1010 inches tall is growing 33 inches per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?\newlineThe two trees will both be _\_ inches tall in _\_ months.

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 substitution: word problemsright chevron icon

Full solution

Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineBobby has been planting young trees in his garden. The maple tree that is 1414 inches tall is growing 22 inches per month, whereas the oak tree that is 1010 inches tall is growing 33 inches per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?\newlineThe two trees will both be _\_ inches tall in _\_ months.
  1. Maple Tree Equation: Let xx represent the number of months and yy represent the height of the trees in inches. \newlineFor the maple tree: \newlineInitial height: 1414 inches \newlineGrowth rate: 22 inches per month \newlineEquation based on the given information: \newlineHeight in inches = growth rate per month ∗* number of months + initial height \newliney=2x+14y = 2x + 14 \newlineFor the maple tree, the equation is: y=2x+14y = 2x + 14
  2. Oak Tree Equation: For the oak tree: \newlineInitial height: 1010 inches \newlineGrowth rate: 33 inches per month \newlineEquation based on the given information: \newlineHeight in inches = growth rate per month ×\times number of months + initial height \newliney=3x+10y = 3x + 10 \newlineFor the oak tree, the equation is: y=3x+10y = 3x + 10
  3. System of Equations: System of equations: \newliney=2x+14y = 2x + 14 \newliney=3x+10y = 3x + 10 \newlineTo find when the trees will be the same height, set the two equations equal to each other. \newline2x+14=3x+102x + 14 = 3x + 10
  4. Solving for x: Solve for x by isolating the variable. \newlineSubtract 2x2x from both sides of the equation: \newline2x+14−2x=3x+10−2x2x + 14 - 2x = 3x + 10 - 2x \newline14=x+1014 = x + 10 \newlineNow, subtract 1010 from both sides: \newline14−10=x+10−1014 - 10 = x + 10 - 10 \newline4=x4 = x \newlineSo, x=4x = 4
  5. Substitute xx into Equation: Now that we have x=4x = 4, we can find the height yy by substituting xx into one of the original equations. \newlineSubstitute 44 for xx in y=2x+14y = 2x + 14: \newliney=2(4)+14y = 2(4) + 14 \newliney=8+14y = 8 + 14 \newliney=22y = 22 \newlineSo, y=22y = 22
  6. Final Result: We have found that x=4x = 4 and y=22y = 22. This means that in 44 months, both the maple and oak trees will be 2222 inches tall.

More problems from Solve a system of equations using substitution: 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 (39)

Related topics

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