Transcript Solving Word Problems using a System of Equations

Do Now
Solve each system using Elimination.
1. 2x + 3y = 8
x – y=2
2. x – 2y = 5
3x – 5y = 8
3. -5x + 8y = 21
10x + 3y = 15
Solving Systems of Linear Equations:
Word Problems
Objective: Set up a system of equations to describe a given
situation, and solve using elimination or substitution
Solving Word Problems with 2
Variables
Step 1: Identify the Variables
 State exactly what each variable represents
 Ex: “Let x = # of dimes and y = # of quarters”
Step 2: Write the Equations


Write two equations
Each sentence/phrase will translate into an equation
Step 3: Solve the System of Equations

Use elimination or substitution
Step 4: Answer the question
Step 5: Check
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
Make sure the solution actually works
Reject any inappropriate answers
Examples
 Ex 1: The sum of two numbers is 18. The sum of the
greater number and twice the smaller number is 25.
Find the numbers.
Step 1: Identify the variables
Let x = the greater number
y = the smaller number
Step 2: Write the equations:
x + y = 18
x + 2y = 25
Step 3: Use substitution or elimination to solve.
Step 4: Answer the question:
x = 11, the greater number
y = 7, the smaller number
Step 5: Check
Examples
 Ex: Suppose a band at another school sells erasers for $2 per
package and pencils for $5 per package. The band sells 220
packages in all and earns a total of $695. Write a system of
equations to find the number of each type of package sold.
Step 1: Let x = packages of erasers
y = packages of pencils
Step 2: x +
y = 220
2x + 5y = 695
Step 3: Solve the equations.
Step 4: Answer the question.
x = 135 packages of erasers
y = 85 packages of pencils
Step 5: Check.
Try It!
On one day, the Rock and Roll Hall of Fame in Cleveland, Ohio,
admitted 4400 adults and students and collected $57,200 in ticket sales.
The price of admission is $14 for an adult and $10 for a student. How
many adults and how many students were admitted to the museum that
day?
Try It!
On one day, the American Museum of Natural History in New York City,
admitted 541 adults and children and collected $9020 in ticket sales.
The price of admission is $40 for an adult and $11 for a child. Find how
many adults and children were admitted to the museum on that day.