Chapter 4
4.3: Real-World Problems: Algebraic Equations
Objective…
Part A: Solve Real-World Problems Algebraically
1)
Shirley wants to frame a drawing in the frame show below. The border of the frame is
x inches wide. The dimensions of the drawing are 12 inches by 5 inches. If the outer
perimeter of the frame is 58 inches, find the width of the frame border.
a. Write an algebraic equation:
b. Solve it:
2)
c. Check your work:
Lisa wrote a riddle: A positive number is 1/3 of another positive number. If their
difference is 48, find the two positive numbers.
a. Write an algebraic equation:
b. Solve it:
c. Check your work:
Chapter 4
4.3: Real-World Problems: Algebraic Equations
3)
Mark wrote a riddle: A negative number is 2/5 of another negative number. If the sum
of the two negative numbers is -35, find the two negative numbers.
a. Write an algebraic equation:
b. Solve it:
4)
c. Check your work:
A theater is divided into a red section and a blue section. The red section has 350
seats and the rest of the seats are in the blue section. A ticket for a red section seat
costs $75 and a ticket for a blue section seat costs $50.
a. Write an expression for the total amount collected from the sale of tickets for all
the seat in the two sections:
b. The total sales when all the tickets are sold are $68,750. How many seats are in
the blue section?
Chapter 4
4.3: Real-World Problems: Algebraic Equations
5)
At an auditorium, tickets are sold for “circle seats” and “row seats.” There are 220
circle seats and the rest are row seats. Each circle seat ticket costs $100 and each
row seat ticket costs $60.
a. Write an expression for the total amount collected from the sale of all the seats at
the auditorium:
b. The total amount collected when all the tickets are sold is $68,000. How many row
seat tickets were sold?
6)
Jared has 12 more comic books than Zoe. If they have 28 comic books altogether find
the number of comic books Jared has.
a. Draw a bar model:
c. Solve it:
b. Write an algebraic equation:
7)
d. Check your work:
James has 16 more game cards than Fay. If they have 48 game cards altogether find
the number of game cards James has.
a. Draw a bar model:
c. Solve it:
b. Write an algebraic equation:
d. Check your work: