1. 4.3: Real-World Problems Algebraic Equations

2. Solve a word problem using bar models
Lisa wrote a riddle: A positive number is 1 3 of another positive number. If their difference is 48, find the two positive numbers.
2 units→ 48
1 unit → = 24
3 units → 24 · 3 = 72
Second Number
First
Number
The two positive numbers are 72 and 24.

3. Solve a word problem using algebraic reasoning
Lisa wrote a riddle: A positive number is 1 3 of another positive number. If their difference is 48, find the two positive numbers.
Let one number be represented by 𝑥.
The other number is of the first number so let the other number be represented by 𝑥.
𝑥− 1 3 𝑥=48
3 3 𝑥− 1 3 𝑥=48
2 3 𝑥=48
3 2 ∙
∙ 3 2
𝑥=72
Second Number
If one number is 72, the other number is 1 3 ∙72=24 .
First Number
The two positive numbers are 72 and 24.

4. Solve a word problem using bar models
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.
7 units→ −35
1 unit → −35 7 = −5
2 units → −5 ∙2=−10
5 units → −5 ∙5=−25
First Number
Second Number
The two negative numbers are −10 and −25.

5. Solve a word problem using algebraic reasoning
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.
Let one number be represented by 𝑥.
The other number is of the first number so let the other number be represented by 𝑥.
𝑥 𝑥=−35
5 5 𝑥+ 2 5 𝑥=−35
7 5 𝑥=−35
5 7 ∙
∙ 5 7
𝑥=−25
Second Number
If one number is -25, the other number is 2 5 ∙ −25 =−10.
First Number
The two positive numbers are −25 and −10.

6. Solve a real-world problem using bar models and algebraic reasoning
Jared has 12 more comic books than Zoe. If they have 28 comic books altogether, find the number of comic books Jared has.
𝑥+12 +𝑥= 28
2𝑥+12= 28
−12
−12
2𝑥= 16
Zoe has 8 comic books. Jared has 12 more than Zoe, so Jared has 8+12 = 20 comic books. 2 2
𝑥= 8

7. Solve a real-world problem using bar models and algebraic reasoning
James has 16 more game cards than Fay. If they have 48 game cards altogether, find the number of game cars James has.
𝑥+16 +𝑥= 48
2𝑥+16= 48
−16
−16
2𝑥= 32
Fay has 16 game cards. James has 16 more than Fay, so James has = 32 game cards. 2 2
𝑥= 16

8. Solve a real- world problem using a table
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 $50. a) Write an expression for the total amount collected from the sale of tickets for all the seats in the two sections.
Type of Ticket
Red
Blue
Ticket Price ($) 75 50
# of Tickets
350 x
Ticket Sales ($)
75·350= 26,250
50·x= 50x 𝑥

9. Solve a real- world problem using a table
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. b) The total sales when all the tickets are sold are $68,750. How many seats are in the blue section?
Type of Ticket
Red
Blue
Ticket Price ($) 75 50
# of Tickets
350 x
Ticket Sales ($)
75·350= 26,250
50·x= 50x 𝑥=
−26250
−26250
50𝑥=42500 50 50
𝑥=850
There are 850 seats in the blue section.