Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. $\newline$ Two fifth grade classes are attending an amusement park as a field trip. Their teachers purchased the tickets for the class and the parent chaperones. Mrs. Randolph purchased $30$ child tickets and $23$ adult tickets, which cost a total of $\$1,359$ . Mr. Kent purchased $1$ adult ticket, paying a total of $\$33$ . What are the ticket prices? $\newline$ The price of a child ticket is $\$\_\_\_\_$ and the price of an adult ticket is $\$\_\_\_\_$ .

View step-by-step help

View step-by-step help

Solve a system of equations using elimination: word problems

Full solution

Q. Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.

\newline

Two fifth grade classes are attending an amusement park as a field trip. Their teachers purchased the tickets for the class and the parent chaperones. Mrs. Randolph purchased

30

child tickets and

23

adult tickets, which cost a total of

\$1,359

. Mr. Kent purchased

1

adult ticket, paying a total of

\$33

. What are the ticket prices?

\newline

The price of a child ticket is

\$\_\_\_\_

and the price of an adult ticket is

\$\_\_\_\_

.

Define Variables: Let $x$ be the price of a child ticket and $y$ be the price of an adult ticket. $\newline$ Mrs. Randolph's purchase: $30x + 23y = 1359$ $\newline$ Mr. Kent's purchase: $x + y = 33$
Create Augmented Matrix: Write the system of equations as an augmented matrix: $\newline$ \begin{array}{cc|c} 30 & 23 & 1359 \ 1 & 1 & 33 \end{array}
Transform to Row-Echelon Form: Use row operations to transform the matrix into row-echelon form. $\newline$ First, swap the rows so the smaller coefficient of $x$ is in the top row. $\newline$ \begin{align*}\(\newline&\begin{array}{cc|c} $\newline$ 1 & 1 & 33 (\newline\)30 & 23 & 1359 $\newline$ \end{array} $\newline$ \end{align*}\)
Eliminate Variable $x$ : Multiply the first row by $-30$ and add it to the second row to eliminate $x$ from the second row. $\newline$ $-30 \times (1 1 | 33) + (30 23 | 1359) = (0 -7 | -33 + 1359)$ $\newline$ This results in the new second row: $(0 -7 | 1326)$
Solve for Variable $y$ : Divide the second row by $-7$ to solve for $y$ . $\newline$ $(0 -7 | 1326) / -7 = (0 1 | -189)$ $\newline$ This gives us $y = -189$ , which is incorrect because ticket prices can't be negative.

More problems from Solve a system of equations using elimination: word problems

Question

Solve using elimination.

\newline

x + 6y = -15

\newline

-2x + 6y = 12

\newline

(\_,\_)

Posted 2 months ago

Question

(1,1)

a solution to this system of equations?

\newline

8x + y = 9

\newline

6x + 12y = 18

\newline

\newline

\newline

Posted 1 month ago

Question

How many solutions does the system of equations below have?

\newline

7

\newline

7

\newline

\newline

\text{[A]no solution}

\newline

\text{[B]one solution}

\newline

\text{[C]infinitely many solutions}

Posted 1 month ago

Question

Which describes the system of equations below?

\newline

y = \frac{1}{7}x - 10

\newline

y = \frac{1}{7}x - 10

\newline

\newline

\text{[A]consistent and independent}

\newline

\text{[B]consistent and dependent}

\newline

\text{[C]inconsistent}

Posted 1 month ago

Question

Solve using substitution.

\newline

y = -5

\newline

-4x + 3y = 17

\newline

Posted 1 month ago

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

\newline

Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Bryan can read

2

pages per minute, and he had already read

98

pages. Jayla, who has a reading speed of

3

pages per minute, had read

48

pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?

\newline

\_\_\_\_

minutes, Bryan and Jayla had each read

\_\_\_\_

Posted 1 month ago

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

At the Castroville Ice Cream Parlor, one group of friends ordered

1

small serving of ice cream and

3

large servings of ice cream for

20

. Another group of friends ordered

1

small serving of ice cream and

4

large servings of ice cream for

26

. How much does the ice cream cost?

\newline

The ice cream costs `\$`_____ for a small serving and `\$`_____ for a large serving.

Posted 1 month ago

Question

\newline

y = -1

\newline

-2x - 4y = 8

\newline

(_____ , _____)

Posted 1 month ago

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

There are two mystery numbers. The sum of

3

times the first number and

3

times the second number is

-18

2

times the first number and

3

times the second number is

-13

. What are the two numbers?

\newline

The first number is ______ , and the second number is ______.

Posted 1 month ago

Question

A teacher purchased

300

colored pencils for an upcoming project. The pencils she ordered come in packs of

20

30

14

packs in all. Write a system of equations to find the number of

20

(x)

30

(y)

the art teacher ordered.

Posted 2 months ago