RATIONAL WORD PROBLEMS.

Slides:



Advertisements
Similar presentations
UNIT II.1 Unit Conversions.
Advertisements

Agenda Homework Folders In Warm up
J J EOPARDY Lets Get Ready To Play Some.... Solve One Step Equations Solve Two Step Equations Solve Other Equations Word Problems to Equations
Applications Problem Solving. 6/25/2013 Applications 2 Four-step Method 1. Define variables Name the quantities to be found Write these down Example:
Solving Rational Equations
Warm - Up. Agenda CA Standards: 5.0: 5. Students solve multi-step problems, including word problems, involving linear equations and linear inequalities.
RATIONAL REVIEW. Find the inverse of each function and verify. f(x) = -6x + 3.
6.7 Applications of Rational Expressions. Objective 1 Solve problems about numbers. Slide
Today’s Date: 11/15/11 “Work” Word Problems Notes on Handout.
Math 025 Unit 5 Section 6.7.
Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:
Objective The student will be able to: solve equations using multiplication and division. Designed by Skip Tyler, Varina High School.
Chapter 7 Section 7.
1.3 “Solving Linear Equations” Steps: 1.Isolate the variable. 2.To solve when there is a fraction next to a variable, multiply both sides by the reciprocal.
§ 6.7 Formulas and Applications of Rational Equations.
NO HOMEWORK QUIZ TURN IN WORK!!!!!! Rational Review.
Partial Fractions Day 2 Chapter 7.4 April 3, 2006.
One step equations using multiplication and division.
KAYAKING EXAMPLE 4 Write and solve a linear system During a kayaking trip, a kayaker travels 12 miles upstream (against the current) and 12 miles downstream.
10-7 Using Rational Equations
ACT QUESTION OF THE DAY Part If x = -5, then |x - 7| = A: -12 B: 2 C: 12 D: -2.
Solving Equations Containing First, we will look at solving these problems algebraically. Here is an example that we will do together using two different.
Solving Rational Equations
4-3 Solving Multiplication Equations Standard : PFA Indicator: P9 (same as 4-2)
Objective The student will be able to: solve equations using multiplication and division.
Section 3.2 Solving Equations using Multiplication and Division.
Motion. Everything in the universe is moving. People walk, run, and drive. Molecules and atoms vibrate with energy. Planets rotate and revolve. Motion:
Solving Equations Containing First, we will look at solving these problems algebraically. Here is an example that we will do together using two different.
Solve Fraction Equations. Designed by Skip Tyler, Varina High School EQ: How do we solve equations of fractions using multiplication and division.
ANSWER is 25% of what number ANSWER 40% 4.What percent of 90 is 36? ANSWER d = 4 ANSWER x = Solve:
Using Formulas 3.4 p Using Formulas to Solve Problems A formula is an equation that shows a relationship between values that are represented by.
Objective The student will be able to: solve equations using multiplication and division. Designed by Skip Tyler, Edited by Mr. Nealey.
Lesson 8-6: Solving Rational Equations and Inequalities.
DO NOW. Objective The student will be able to: solve equations using multiplication and division. Designed by Skip Tyler, Varina High School.
1) Solve. -5t = 60 To get the variable by itself, which number needs to be moved? -5 To move the -5, you have to do the opposite operation. What operation.
WARM UP Divide and check SOLVING RATIONAL EXPRESSIONS.
WARM UP 1.Solve 1.If a computer’s printer can print 12 pages in 3 minutes, how many pages can it print in 1 minute? Multiply through by x – x(x.
+ 9-6 Solving Rational Equations Objective: The student will be able to solve rational equations.
Math 154B Final Review Exponents and Polynomials Factoring and Applications Rationals and Applications Roots and Radicals Quadratic Equations
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Objective The student will be able to:
Lesson 3.2 Solving Equations with Multiplication and Division
2-7 Warm Up Problem of the Day Lesson Presentation
HW: Worksheet Aim: How do we solve fractional equation?
Solving Rational Equations
M3U5D5 Warmup Simplify the expression.
Solving Rational Equations
Objective The student will be able to:
1) Solve 2x - 4y = 7 for x + 4y + 4y 2x = 7 + 4y 2 2 Draw “the river”
Objective The student will be able to:
Fractional Equations Chapter 7 Section 7.4.
Solving Word Problems Objective: Students will be able to write and solve equations based on real world situations.
Solving Equations Containing
Objective The student will be able to:
Two-Step Equations Mrs. Book.
Chapter 5 Section 3 Solving Linear Equations with Fractions and Decimals by Clearing the Denominators.
Solving Rational Equations by
P4 Day 1 Section P4.
Solving Rational Equations
Solving Multiplication Equations
Solving Rational Equations by
Solving Fractional Equations
CA Standards: Objectives: Agenda 1.) Warm - Up
Solve equations using multiplication and division.
Objective The student will be able to:
Objective The student will be able to:
Rational Functions: Applications
Concept 5 Rational expressions.
Objective Standard 15.0 I will solve a rational equation by multiplying the LCM of the denominators to both sides.
Section P4.
Presentation transcript:

RATIONAL WORD PROBLEMS

TO SOLVE RATIONAL WORD PROBLEMS

TO SOLVE RATIONAL WORD PROBLEMS 1. Set up the unknowns in one variable.

TO SOLVE RATIONAL WORD PROBLEMS 1. Set up the unknowns in one variable. 2. Set up an equation for the situation.

TO SOLVE RATIONAL WORD PROBLEMS 1. Set up the unknowns in one variable. 2. Set up an equation for the situation. 3. Multiply by the common denominator to clear out fractions.

TO SOLVE RATIONAL WORD PROBLEMS 1. Set up the unknowns in one variable. 2. Set up an equation for the situation. 3. Multiply by the common denominator to clear out fractions. 4. Solve the remaining equation for the variable.

TO SOLVE RATIONAL WORD PROBLEMS 1. Set up the unknowns in one variable. 2. Set up an equation for the situation. 3. Multiply by the common denominator to clear out fractions. 4. Solve the remaining equation for the variable. 5. State final answers in real world terms.

Most tunnels are drilled using tunnel-boring machines that begin at both ends of the tunnel. Suppose a new underwater tunnel is being built and one tunnel-boring machine alone can finish the tunnel in 4 years. A different type of machine can tunnel to the other side in 3 years. If both machines start at opposite ends and work at the same time, when will the tunnel be finished?

Let x = number of years together

Let x = number of years together Equation:

Let x = number of years together Equation:

Solve equation: multiply by common denominator (4)(3)(x).

Solve equation: multiply by common denominator (4)(3)(x).

Solve equation: multiply by common denominator (4)(3)(x).

Solve equation: multiply by common denominator (4)(3)(x).

Solve equation: multiply by common denominator (4)(3)(x).

If both machines work toward each other it will take 1 If both machines work toward each other it will take 1.7 years to finish the tunnel.

If both machines work toward each other it will take 1 If both machines work toward each other it will take 1.7 years to finish the tunnel.

A car travels 300 km in the same time that a freight train travels 200 km. The speed of the car is 20 km/h more than the speed of the train. Find the speed of the car and the speed of the train.

Let x = speed of train Let x + 20 = speed of car A car travels 300 km in the same time that a freight train travels 200 km. The speed of the car is 20 km/h more than the speed of the train. Find the speed of the car and the speed of the train. Let x = speed of train Let x + 20 = speed of car

Let x = speed of train Let x + 20 = speed of car A car travels 300 km in the same time that a freight train travels 200 km. The speed of the car is 20 km/h more than the speed of the train. Find the speed of the car and the speed of the train. Let x = speed of train Let x + 20 = speed of car

Use the formula d = rt. Solve for “t”.

Use the formula d = rt. Solve for “t”. t = d/r

Use the formula d = rt. Solve for “t”. t = d/r

Use the formula d = rt. Solve for “t”. t = d/r

Use the formula d = rt. Solve for “t”. t = d/r

Solve: multiply by the common denominator (x + 20)(x).

Solve: multiply by the common denominator (x + 20)(x).

Solve: multiply by the common denominator (x + 20)(x).

Solve: multiply by the common denominator (x + 20)(x).

Solve: multiply by the common denominator (x + 20)(x).

Speed of train = x = 40 km/h

Speed of train = x = 40 km/h Speed of car = x + 20 = 60 km/h

Speed of train = x = 40 km/h Speed of car = x + 20 = 60 km/h

One electronic reader can read a deck of punched cards in half the time of another reader. Together they can read the deck in 8 minutes. How long would it take each reader alone to read the deck?

Let x = first reader time One electronic reader can read a deck of punched cards in half the time of another reader. Together they can read the deck in 8 minutes. How long would it take each reader alone to read the deck? Let x = first reader time

Let x = first reader time Let 2x = second reader time One electronic reader can read a deck of punched cards in half the time of another reader. Together they can read the deck in 8 minutes. How long would it take each reader alone to read the deck? Let x = first reader time Let 2x = second reader time

Let x = first reader time Let 2x = second reader time One electronic reader can read a deck of punched cards in half the time of another reader. Together they can read the deck in 8 minutes. How long would it take each reader alone to read the deck? Let x = first reader time Let 2x = second reader time

Solve: multiply by common denominator (x)(8)

Solve: multiply by common denominator (x)(8)

Solve: multiply by common denominator (x)(8)

Solve: multiply by common denominator (x)(8) First reader = x = 12 minutes Second reader = 2x = 24 minutes

One pipe can fill a tank in 6 hours while another can empty it in 2 hours. How long will it take to empty the full tank if both pipes are open at once?

Let x = time to empty full tank One pipe can fill a tank in 6 hours while another can empty it in 2 hours. How long will it take to empty the full tank if both pipes are open at once? Let x = time to empty full tank

Let x = time to empty full tank Part empty - Part fill = Total empty One pipe can fill a tank in 6 hours while another can empty it in 2 hours. How long will it take to empty the full tank if both pipes are open at once? Let x = time to empty full tank Part empty - Part fill = Total empty

Let x = time to empty full tank Part empty - Part fill = Total empty One pipe can fill a tank in 6 hours while another can empty it in 2 hours. How long will it take to empty the full tank if both pipes are open at once? Let x = time to empty full tank Part empty - Part fill = Total empty

Solve: multiply by the common denominator (x)(6).

Solve: multiply by the common denominator (x)(6).

Solve: multiply by the common denominator (x)(6).

Solve: multiply by the common denominator (x)(6).

Solve: multiply by the common denominator (x)(6). It will take 3 hours to empty the tank.

TO SOLVE RATIONAL WORD PROBLEMS 1. Set up variables. 2. Set up equation. 3. Multiply by the common denominator. 4. Solve for variables. 5. Define final answers.

PRACTICE TIME GO FOR IT!!!!