• ACTIVITY 13 Learning Objectives: Lesson 13-3

Lesson 13-3
Modeling and Solving Subtraction Equations
ACTIVITY 13
continued
My Notes
Learning Objectives:
Write a subtraction equation to represent a situation.
Solve a subtraction equation of the form x − a = b, where a, b, and x
are all nonnegative rational numbers.
•
•
SUGGESTED LEARNING STRATEGIES: Summarizing, Think-PairShare, RAFT, Self Revision/Peer Revision, Work Backward
Many real-world problems can be represented and solved using a
subtraction equation very much like those represented and solved using
an addition equation.
Example E
Step 1:
Define a variable.
Let x represent the number of applications she had to
begin with.
Step 2:
Write a verbal model.
number of apps she had to begin with − 7 = 17
Step 3:
Write an equation.
x − 7 = 17
Step 4:
Use mental math to solve the equation.
From what number can you subtract 7 and get 17?
x = 24
Step 5:
Use substitution to check the solution.
24 − 7 = 17
17 = 17
Solution: Samantha had 24 apps to begin with.
Try These E
Shiro is driving from Houston, Texas, to San Antonio, Texas. After
driving 50 miles, he still has 150 miles to go. How many miles is the trip
from Houston to San Antonio?
a. Define a variable, write a verbal model and an equation.
b. Solve the equation and check using substitution.
166
Unit 3 • Expressions and Equations
© 2014 College Board. All rights reserved.
Samantha has apps on her tablet. If she deletes 7 of them she will have
17 left. How many apps did she have to begin with?
Lesson 13-3
Modeling and Solving Subtraction Equations
ACTIVITY 13
continued
1. After Yadra lent $9.12 to Raquel, she had $24.36 left. How much
money did Yadra have before the loan? Define a variable and write a
verbal model and equation for this situation. Then solve the equation
and check the solution.
My Notes
2. Samantha was entering her contacts on her new tablet. She has
entered 25 contacts and still has 22 left to enter. How many total
contacts will she have on her tablet? Define a variable and write a
verbal model and equation for this situation. Then solve the equation
and check the solution.
© 2014 College Board. All rights reserved.
3. Confirm your solution to the equation in Item 2 by using the balance
scale method.
4. Critique the reasoning of others. Joshua believes a subtraction
equation can be solved using a balance scale by subtracting a number
from each side. Is he correct? Explain.
Activity 13 • Solving Addition and Subtraction Equations
167
Lesson 13-3
Modeling and Solving Subtraction Equations
ACTIVITY 13
continued
My Notes
Check Your Understanding
5. Enzo still owes $750 on his new furniture. He has already paid $600
on it. What was the original cost of the furniture? Define a variable
and write a verbal model and equation for this situation. Then solve
the equation and check the solution.
6. Yusra’s dog is overweight. The vet says the dog needs to lose
7 pounds to get down to the desirable weight of 45 pounds. How
much does Yusra’s dog weigh? Define a variable and write a verbal
model and equation for this situation. Then solve the equation and
check the solution.
LESSON 13-3 PRACTICE
8. Model with mathematics. Payat put $420 from his savings
account into a certificate of deposit to earn more interest. He then
had $80 left in his savings account. How much did Payat have in his
savings account before he opened the certificate? Define a variable
and write a verbal model and equation for this situation. Then solve
the equation and check the solution.
9. Critique the reasoning of others. Marsha said she could solve
x − 3 = 7 using the balance scale method by adding 3 to each side of
the scale. Do you think her reasoning is correct? Explain.
168
Unit 3 • Expressions and Equations
© 2014 College Board. All rights reserved.
7. You see a coat on sale for $78. The sign says that the price is $15 off
the original price. What was the original price? Define a variable and
write a verbal model and equation for this situation. Then solve the
equation and check the solution.