50+ Math Word Problems worksheets for 8th Grade on Quizizz | Free ... - Free Printable

Problem Analysis and Solutions

The provided image contains four word problems related to systems of equations. Each problem requires setting up a system of equations based on the given information. Below, I will solve each problem step by step.

---

Problem 1:

Question:
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represent the system that could be used?

#### Solution:
Let:
- \( s \) = cost of one senior citizen ticket (in dollars)
- \( c \) = cost of one child ticket (in dollars)

From the problem:
1. On the first day: \( 3s + c = 38 \)
2. On the second day: \( 3s + 2c = 52 \)

Thus, the system of equations is:
\[
\begin{cases}
3s + c = 38 \\
3s + 2c = 52
\end{cases}
\]

#### Correct Answer:
\[
\boxed{D}
\]

---

Problem 2:

Question:
Last season, two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let \( x \) and \( y \) represent the number of yards each individual player rushed. Which system of equations could be used?

#### Solution:
Let:
- \( x \) = yards rushed by the first player
- \( y \) = yards rushed by the second player

From the problem:
1. Combined total yards: \( x + y = 1550 \)
2. One player rushed 4 times as many yards as the other: \( y = 4x \)

Thus, the system of equations is:
\[
\begin{cases}
x + y = 1550 \\
y = 4x
\end{cases}
\]

#### Correct Answer:
\[
\boxed{B}
\]

---

Problem 3:

Question:
Dennis mowed his next-door neighbor's lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job, he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

#### Solution:
Let:
- \( d \) = number of dimes
- \( n \) = number of nickels

From the problem:
1. Total number of coins: \( d + n = 80 \)
2. Total value of coins: \( 0.10d + 0.05n = 6.60 \)

Thus, the system of equations is:
\[
\begin{cases}
d + n = 80 \\
0.10d + 0.05n = 6.60
\end{cases}
\]

#### Correct Answer:
\[
\boxed{B}
\]

---

Problem 4:

Question:
On Monday, Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday, he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

#### Solution:
Let:
- \( c \) = cost of one cup of coffee (in dollars)
- \( d \) = cost of one doughnut (in dollars)

From the problem:
1. On Monday: \( 10c + 5d = 16.50 \)
2. On Tuesday: \( 5c + 10d = 14.25 \)

Thus, the system of equations is:
\[
\begin{cases}
10c + 5d = 16.50 \\
5c + 10d = 14.25
\end{cases}
\]

#### Correct Answer:
\[
\boxed{C}
\]

---

Final Answers:

1. \(\boxed{D}\)
2. \(\boxed{B}\)
3. \(\boxed{B}\)
4. \(\boxed{C}\)