Let's solve this
word problem step by step and explain the solution clearly.
---
🎯 Problem Statement:
The school sold tickets for a talent show:
- On
Day 1:
- 4 senior citizen tickets
- 5 student tickets
- Total revenue =
$102
- On
Day 2:
- 7 senior citizen tickets
- 5 student tickets
- Total revenue =
$126
We are to find:
- The price of
one senior citizen ticket (let’s call it $ C $)
- The price of
one student ticket (let’s call it $ S $)
---
✔ Step 1: Set up the system of equations
From Day 1:
$$
4C + 5S = 102 \quad \text{(Equation 1)}
$$
From Day 2:
$$
7C + 5S = 126 \quad \text{(Equation 2)}
$$
---
✔ Step 2: Solve the system using elimination
We can eliminate one variable. Notice that both equations have $ 5S $. So, subtract Equation 1 from Equation 2:
$$
(7C + 5S) - (4C + 5S) = 126 - 102
$$
$$
7C + 5S - 4C - 5S = 24
$$
$$
3C = 24
$$
$$
C = \frac{24}{3} = 8
$$
✔ So, the
senior citizen ticket costs $8.
---
✔ Step 3: Plug back to find $ S $
Use Equation 1:
$$
4C + 5S = 102
$$
Substitute $ C = 8 $:
$$
4(8) + 5S = 102
$$
$$
32 + 5S = 102
$$
$$
5S = 102 - 32 = 70
$$
$$
S = \frac{70}{5} = 14
$$
✔ So, the
student ticket costs $14.
---
✔ Final Answer:
-
Senior citizen ticket: $ \boxed{8} $
-
Student ticket: $ \boxed{14} $
---
🔍 Verification:
Check both days:
-
Day 1: $ 4(8) + 5(14) = 32 + 70 = 102 $
✔
-
Day 2: $ 7(8) + 5(14) = 56 + 70 = 126 $
✔
Perfect!
---
📝 Summary:
You correctly solved the system using
elimination, and your work shows:
- Subtracting the equations to eliminate $ S $
- Solving for $ C = 8 $
- Substituting back to get $ S = 14 $
✔ Your answer is
correct! The senior citizen ticket is
$8, and the student ticket is
$14.
Parent Tip: Review the logic above to help your child master the concept of word problems kuta software.
