Lesson Using systems of equations to solve problems on tickets
Algebra
->
Coordinate Systems and Linear Equations
-> Lesson Using systems of equations to solve problems on tickets
Log On
Linear Solvers
Linear
Practice
Practice
Answers archive
Answers
Word Problems
Word
Lessons
Lessons
In depth
In
Source code of 'Using systems of equations to solve problems on tickets'
This Lesson (Using systems of equations to solve problems on tickets)
was created by by
ikleyn(52781)
:
View Source
,
Show
About ikleyn
:
<H2>Using systems of equations to solve problems on tickets</H2> <H3>Problem 1</H3>Adult tickets for a concert cost $8 each and student tickets cost $5 each. A total of 55 tickets were sold worth $365. How many adult and student tickets were sold? <B>Solution</B> <pre> Let "x" be the number of adult tickets sold and let "y" be the number of student tickets sold. Then from the condition you have this system of two equations in two unknowns x + y = 55, (1) 8x + 5y = 365. (2) Express x = 55 - y from (1) and substitute it into equation (2). You will get 8*(55 - y) + 5y = 365. Simplify and solve for y: 440 - 8y + 5y = 365, -3y = 365 - 440 ====> -3y = -75 ====> y = {{{(-75)/(-3)}}} = 25. Then x = 55 - 25 = 30. </pre> <B>Answer</B>. 30 adults tickets and 25 adults tickets. <U>Check</U>. 25*5 + 30*8 = 125 + 240 = 365. ! Correct ! The method I used to solve the system of equations in this problem was the <U>Substitution method</U>. <H3>Problem 2</H3>A movie theater charges $5 admission for an adult and $3 for a child. If 700 tickets were sold and the total revenue received was $2900, how many tickets of each type were sold? <B>Solution</B> <pre> Let "a" be the number of adult tickets sold and let "c" be the number of adult tickets sold. Then from the condition you have this system of two equations in two unknowns a + c = 700, (1) 5a + 3c = 2900. (2) Express a = 700 - c from (1) and substitute it into equation (2). You will get 5*(700 - c) + 3c = 2900. Simplify and solve for c: 3500 - 5c + 3c = 2900, -2c = 2900 - 3500 ====> -2c = - 600 ====> c = {{{(-600)/(-2)}}} = 300. Then a = 700 - 300 = 400. </pre> <B>Answer</B>. 300 children tickets and 400 adults tickets. <U>Check</U>. 300*3 + 400*5 = 900 + 2000 = 2900. ! Correct ! The method I used to solve the system of equations in this problem was the Substitution method. <H3>Problem 3</H3>If 104 people attend a concert and tickets for adults cost $2.255 while tickets for children cost $1.75 and total receipts for the concert was $202.5, how many of each went to the concert? <B>Solution</B> <pre> Let "x" be the number of the adult ticket bought, and let "y" be the number of the children ticket bought. Then you have a system of two linear equations in two unknowns x + y = 104, (1) 225x + 175y = 20250. (2) (this is the "value" equation in cents) From the equation (1), express y = 104-x, and substitute this expression into the equation (2). You will get 225*x + 175(104-x) = 20250. (3) The equation (3) is a single equation for the single unknown "x". Reduce all terms in both sides by the factor of 25 : 9x + 7*(104-x) = 810. 9x + 728 - 7x = 810, 2x = 810 - 728, 2x = 82 ---> x = {{{82/2}}} = 41. <B>Answer</B>. 41 adult tickets and 104-41 = 63 children tickets. </pre> My other lessons in this site on solving systems of two linear equations in two unknowns (Algebra-I curriculum) are - <A HREF = http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-system-of-two-eqns-by-the-Subst-method.lesson>Solution of the linear system of two equations in two unknowns by the Substitution method</A> - <A HREF = http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-Elimination-method.lesson>Solution of the linear system of two equations in two unknowns by the Elimination method</A> - <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-using-det.lesson>Solution of the linear system of two equations in two unknowns using determinant</A> - <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Geom-interpret-of-the-lin-system-of-two-eqns-with-two-unknowns.lesson>Geometric interpretation of the linear system of two equations in two unknowns</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Useful-tricks-when-solving-systems-of-2-eqns-in-2-unknowns-by-the-Subst-method.lesson>Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method</A> - <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Solving-word-probs-using-linear-systems-of-two-eqns-with-two-unknowns.lesson>Solving word problems using linear systems of two equations in two unknowns</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Word-problems-that-lead-to-a-simple-system-of-two-equations-in--wo-unknowns.lesson>Word problems that lead to a simple system of two equations in two unknowns</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/Oranges-and-Grapefruits.lesson >Oranges and grapefruits</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Three-methods-for-solving-standard-typical-problem-on-tickets.lesson>Three methods for solving standard (typical) problems on tickets</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Using-systems-of-equations-to-solve-problems-on-SHARES.lesson>Using systems of equations to solve problems on shares</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Using-systems-of-equations-to-solve-problems-on-investment.lesson>Using systems of equations to solve problems on investment</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Two-mechanics-work-on-a-car.lesson>Two mechanics work on a car</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/The-Robinson-family-and-the-Sanders-family-each-used-their-sprinklers-last-summer.lesson>The Robinson family and the Sanders family each used their sprinklers last summer</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Roses-and-violets.lesson>Roses and vilolets</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/Counting-calories-and-grams-of-fat-in-combined-food.lesson>Counting calories and grams of fat in combined food</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/A-theater-group-made-appearances-in-two-cities.lesson>A theater group made appearances in two cities</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Exchange-problems-solved-using-systems-of-linear-equations.lesson>Exchange problems solved using systems of linear equations</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Typical-word-problems-on-systems-of-2-equations-in-2-unknowns.lesson>Typical word problems on systems of 2 equations in 2 unknowns</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/How-to-algebreze-and-to-solve-this-problem-on-2-eqns-in-2-unknwns.lesson>HOW TO algebraize and solve these problems on 2 equations in 2 unknowns</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/One-unusual-problem-to-solve-using-system-of-two-equations.lesson>One unusual problem to solve using system of two equations</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Non-standard-problem-with-a-tricky-setup-.lesson>Non-standard problem with a tricky setup</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/Sometime-one-equations-is-enough-to-find-two-unknowns-by-an-UNIQUE-way.lesson>Sometimes one equation is enough to find two unknowns in a unique way</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Solving-mentally-word-problems-on-two-equations-in-two-unknowns-NEW.lesson>Solving mentally word problems on two equations in two unknowns</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Solving-systems-of-non-linear-equations-by-reducing-to-linear-ones.lesson>Solving systems of non-linear equations by reducing to linear ones</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Solving-word-problems-for-3-unknowns-by-reducing-to-equations-in-2-unknowns.lesson>Solving word problems for 3 unknowns by reducing to equations in 2 unknowns</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/System-of-equations-helps-to-solve-a-problem-for-the-Thanksgiving-day.lesson>System of equations helps to solve a problem for the Thanksgiving day</A> - <A HREF=https://www.algebra.com/algebra/homework/coordinate/Using-system-of-two-equations-to-solve-a-problem-for-the-day-of-April-1.lesson>Using system of two equations to solve the problem for the day of April, 1</A> - <A HREF =https://www.algebra.com/algebra/homework/coordinate/OVERVIEW-of-lessons-on-solving-systems-of-two-linear-equations-in-two-unknowns.lesson>OVERVIEW of lessons on solving systems of two linear equations in two unknowns</A> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-I.
