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.\newlineBrittany just became a personal trainer and is finalizing her pricing plans. One plan is to charge $41\$41 for the initial consultation and then $96\$96 per session. Another plan is to charge $13\$13 for the consultation and then $98\$98 per session. Brittany realizes that the two plans have the same cost for a certain number of sessions. How many sessions is that? What is that cost?\newlineFor _____ sessions, the cost is $\$_____ on either plan.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright 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.\newlineBrittany just became a personal trainer and is finalizing her pricing plans. One plan is to charge $41\$41 for the initial consultation and then $96\$96 per session. Another plan is to charge $13\$13 for the consultation and then $98\$98 per session. Brittany realizes that the two plans have the same cost for a certain number of sessions. How many sessions is that? What is that cost?\newlineFor _____ sessions, the cost is $\$_____ on either plan.
  1. Define Variables: Let's define the variables:\newlineLet xx be the number of sessions.\newlineLet CC be the total cost for the sessions.\newlineWe can write two equations to represent each plan:\newlinePlan 11: C=41+96xC = 41 + 96x\newlinePlan 22: C=13+98xC = 13 + 98x\newlineWe are looking for the number of sessions (xx) where the cost (CC) is the same for both plans.
  2. Set Equations Equal: To solve the system using substitution, we set the two equations equal to each other because they both equal CC at the point where the plans cost the same:\newline41+96x=13+98x41 + 96x = 13 + 98x
  3. Solve for x: Now, we solve for x:\newlineSubtract 96x96x from both sides:\newline41+96x−96x=13+98x−96x41 + 96x - 96x = 13 + 98x - 96x\newline41=13+2x41 = 13 + 2x
  4. Isolate xx: Subtract 1313 from both sides to isolate the term with xx:41−13=13−13+2x41 - 13 = 13 - 13 + 2x28=2x28 = 2x
  5. Calculate Total Cost: Divide both sides by 22 to solve for xx:282=2x2\frac{28}{2} = \frac{2x}{2}14=x14 = x
  6. Final Cost Calculation: Now that we have the number of sessions x=14x = 14, we can find the total cost CC for that number of sessions using either of the original equations. Let's use Plan 11's equation:\newlineC=41+96xC = 41 + 96x\newlineC=41+96(14)C = 41 + 96(14)
  7. Final Cost Calculation: Now that we have the number of sessions x=14x = 14, we can find the total cost CC for that number of sessions using either of the original equations. Let's use Plan 11's equation:\newlineC=41+96xC = 41 + 96x\newlineC=41+96(14)C = 41 + 96(14)Calculate the total cost:\newlineC=41+96(14)C = 41 + 96(14)\newlineC=41+1344C = 41 + 1344\newlineC=1385C = 1385

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 (41)

Related topics

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