4.5 Solving Real World Systems of Equations (Due 2/27/25)
star
star
star
star
star
Last updated 10 months ago
31 questions
Required
20
…
Required
20
…
Required
10
…
Essential Question: How can you solve a system of equations algebraically?
Learning Target: Students will be able to use the elimination and substitution methods to solve a system of equations that represent real-world situations.
Complete the entire assignment and show work for full credit.
Proving Solutions to Systems of Equations
Question 1
1.
Here are two equations:
Equation 1: 5x-2y=15
Equation 2: 6x+4y=34
Is (3,4) a solution to this system of equations? Use complete sentences and support your response with math.
Question 2
2.
Explain or show that the point (5,-4) is a solution to this system of equations:
Using graphs to a solve a real world situation involving a System of Equations
Question 3
3.
Volunteer drivers are needed to bring 80 students to the championship baseball game. Drivers either have cars, which can seat 4 students, or vans, which can seat 6 students.
The equation 4c + 6v = 80 describes the relationship between the number of cars c and number of vans v that can transport exactly 80 students.
Explain how you know that this graph represents this equation.
Creating and Solving a System of Equations
Required
10
Required
5
Required
5
Required
5
Required
5
Required
10
…
Required
10
…
Required
10
…
Required
20
…
Sales Questions
Required
10
Required
5
Required
5
Required
5
Required
10
Required
10
Required
20
Required
2
…
Required
20
Finding Two Numbers
Required
20
Question 22
22.
Solve each word problem using substitution or elimination.
First Number_______
Second Number_______
Required
20
Question 23
23.
Solve each word problem using substitution or elimination.
1st Number _______
2nd Number _______
Substitution Problems
Required
20
Question 24
24.
Solve each word problem using substitution or elimination.
Number of Student who are smart and like their Math teacher _______
Number of students who are mid and like their English teacher _______
Required
20
Required
20
Category Problems
Required
20
Question 27
27.
Solve each word problem using substitution or elimination.
# nickels _______
# dimes _______
Required
20
Question 28
28.
Solve each word problem using substitution or elimination.
# T/F questions _______
# Multiple Choice question _______
Sales Problems
Required
20
Question 29
29.
Solve each word problem using substitution or elimination.
#Adult Tickets_______
#Child Tickets_______
Required
20
Required
20
Question 4
4.
Below is word problem. Which highlighted words or phrases could be variables?
Diego is thinking of two positive whole numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
Question 5
5.
Below is word problem. Which highlighted word or phrase means "multiply by 3"?
Diego is thinking of two positive whole numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
Question 6
6.
Below is word problem. Which highlighted word or phrase means "multiply by 2"?
Diego is thinking of two positive whole numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
Question 7
7.
Below is word problem. Which highlighted word or phrase means "addition"?
Diego is thinking of two positive whole numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
Question 8
8.
Below is word problem. Which highlighted word or phrase means "equal to"?
Diego is thinking of two positive whole numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
Question 9
9.
Diego is thinking of two positive whole numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
Write an equation that represents Diego's description.
Question 10
10.
Diego is thinking of two positive whole numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
Find two possible pairs of numbers Diego could be thinking of. (There are several possibilities.)
1st Pair of numbers (# and #):
_______
2nd Pair of numbers (# and #):
_______
Question 11
11.
Diego is thinking of two positive whole numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
Diego then says, “If we take half of the first number and double the second, the sum is 14.”
Write an equation that could represent his second equation.
Question 12
12.
Diego is thinking of two positive numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
Diego then says, “If we take half of the first number and double the second, the sum is 14.”
What are Diego’s two numbers?
1st Number _______
2nd Number _______
Problem #1
Question 13
13.
Below is word problem. Which highlighted words or phrases are the variables of this real world problem?
A school is selling tickets for a play. Student tickets cost $5 each, and adult tickets cost $8 each. A total of 135 tickets were sold, bringing in $855 in sales. How many student and adult tickets were sold?
Question 14
14.
Below is word problem. Which highlighted word or phrase means "multiply by 5"?
A school is selling tickets for a play. Student tickets cost $5 each, and adult tickets cost $8 each. A total of 135 tickets were sold, bringing in $855 in sales. How many student and adult tickets were sold?
Question 15
15.
Below is word problem. Which highlighted word or phrase means "multiply by 8"?
A school is selling tickets for a play. Student tickets cost $5 each, and adult tickets cost $8 each. A total of 135 tickets were sold, bringing in $855 in sales. How many student and adult tickets were sold?
Question 16
16.
Below is word problem. Which highlighted word or phrase means "addition" and "equal to" at the same time?
A school is selling tickets for a play. Student tickets cost $5 each, and adult tickets cost $8 each. A total of 135 tickets were sold, bringing in $855 in sales. How many student and adult tickets were sold?
Question 17
17.
Write an equation to show how much money the school made in ticket sales.
_______
Question 18
18.
Write an equation to show how many
tickets the school sold.
_______
Question 19
19.
Solve each word problem using substitution or elimination.
Number of student tickets_______
Number of adult tickets _______
Problem #2
Question 20
20.
The knitting club sold 40 scarves and hats at a winter festival and made $700 from the sales. They charged $18 for each scarf and $14 for each hat.
If s represents the number of scarves sold and h represents the number of hats sold, which system of equations represents the constraints in this situation?
Question 21
21.
Solve each word problem using substitution or elimination.
The knitting club sold 40 scarves and hats at a winter festival and made $700 from the sales. They charged $18 for each scarf and $14 for each hat.
If s represents the number of scarves sold and h represents the number of hats sold, which system of equations represents the constraints in this situation?
Number of Scarves _______
Number of Hats _______
Question 25
25.
Solve each word problem using substitution or elimination.
Number of general admission tickets sold _______
Number of VIP tickets sold _______
Question 26
26.
Solve each word problem using substitution or elimination.
Number of roses _______
Number of tulips _______
Question 30
30.
Solve each word problem using substitution or elimination.
# Hot Dogs _______
# Pizza Slices _______
Question 31
31.
Solve each word problem using substitution or elimination.