Write and Solve Multi-Step Equations
The English class, consisting of 18 students, is going to a bookstore. Each student will buy a book and a bookmark. The History class, consisting of 10 students, is going to a café. Each student will buy a drink and a pastry. The bookmark costs $2.75, the café drink costs twice as much as the bookstore book, and the pastry costs $3.35.
Question: What is the cost of the bookstore book?
18(x + 2.75) = 10(2x + 3.35)
x = $8
Is it infinite solution, no solution, or one solution?6(a+4)=3(2a+8)
24 = 24
infinite solution
5x−4≤11
x ≤ 7/5
x ≤ 1.4
Jake has already saved $20 from selling lemonade. He earns $8 for each pitcher he sells. He wants to have at least $60 to buy a new backpack. Write and solve an inequality to determine how many pitchers Jake needs to sell to reach his goal. Then interpret the solution.
20 + 8x ≥ 60
x ≥ 5
5(4y−1)=3(6y+2)
y = 5.5
Is it infinite solution, no solution, or one solution?5(2x+3)=10(x+4)
15 = 40
No Solution
0.6x + 4.2 > 7.8
x > 6
Sophie has already saved $50 from doing chores. She earns $15 for each lawn she mows. She wants to have at least $125 to buy a new bicycle.
50 + 15x ≥ 125
x ≥ 6
A basketball team of 10 players is going to a theme park. Each player will buy a ticket and a snack. The volleyball team of 8 players is going to a movie theater. Each player will buy a ticket and a popcorn combo. The snack costs $4.00, and the movie theater ticket costs $1.50 more than the theme park ticket. The popcorn combo costs $3.50.
Question: What is the cost of the theme park ticket?
10(x + 4.00) = 8(1.50x + 3.50)
x = $6.00
Is it infinite solution, no solution, or one solution?6(x−3)=7(2x+1)
One Solution
7x−5>23
x > 4
Ethan has $60 from his allowance. He buys lunch for $5 from the school. He wants to have at least $15 to buy a new game.
60 - 5x ≥ 15
x ≤ 9
5(x − 6) = 3(3.5x - 5)
x = 18
Is it infinite solution, no solution, or one solution?2(3m+4)=6(m+5)
8 = 30
No Solution
4/5x + 7/15 ≥ 9/10
x ≥ 1 17/24
Lily has $70 saved from birthday money. She buys pet toys for $6 for each. She wants to have at least $22 to go to a pet show.
70 - 6x ≥ 22
x ≤ 9
A group of 14 campers is buying notebooks and pencils. Another group of 16 campers is buying folders and pens. Each pencil costs $0.75, each pen costs $1.20, and the folder 0.8 times the price of a notebook Question: What is the cost of one notebook if each group spent the same cost?
14(x + 0.75) = 16(0.8x + 1.20)
x = $7.25
Is it infinite solution, no solution, or one solution?2(m+9)= 2m+18
18 = 18
Infinite Solution
7 - 3x ≥ 19
x ≤ -4
Noah has $40 from doing small jobs for neighbors. He earns $10 for each bag of groceries he delivers. He wants at least $100 to buy a new skateboard.
40 + 10x ≥ 100
x ≥ 6