Problem 1 :
Amanda rented a bike from Shawna's Bikes. They charged her $2 per hour, plus a $10 fee. Amanda paid less than $27.
a) Write an inequality to represent the situation. Be sure to define your variable.
b) Solve the inequality to find the maximum number of hours Amanda rented the bike.
Solution :
Fee = $10
Charge per hour = $2
Let x be the number of hours rented.
2x + 10 < 27
2x < 27 - 10
2x < 17
x < 17/2
x < 8.5
So, the maximum number of hours is 8.5.
Problem 2 :
You need to buy some pencils and an eraser. You can spend no more than $5. The eraser costs $1 and the pencils cost $0.25 each.
a) Write an inequality to represent the situation. Be sure to define your variable.
b) Solve the inequality to find the maximum number of pencils you can buy.
Solution :
No more than 5 means, lesser than 5 only is possible.
Cost of each eraser = $1, cost of each pencil = $0.25
Let x be the number of pencils
1 + 0.25x < 5
0.25x < 5 - 1
0.25x < 4
x < 4/0.25
x < 16
The maximum number of pencils he can buy is 16.
Problem 3 :
Mark's Canoes rents canoes for $20 plus $35 per hour. You do not want to spend more than $150. For how many hours can you afford to rent the canoe?
a) Write an inequality to represent the situation. Be sure to define your variable.
b) Solve the inequality and answer the question.
Solution :
No more than 150, means less than 150.
Let x be the number of hours.
20 + 35x < 150
35x < 150 - 20
35x < 130
x < 130/35
x < 3.7
So, the maximum number of hours is 3.7
Problem 4 :
For a field trip 18 students rode in cars and the rest filled five buses. How many students were in each bus if no more than 250 students went on the trip?
a) Write an inequality to represent the situation. Be sure to define your variable.
b) Solve the inequality and answer the question.
Solution :
Let x be the number of students travelled in each 5 buses.
18 + 5x ≤ 250
5x ≤ 250 - 18
5x ≤ 232
x ≤ 232/5
x ≤ 46.4
So, the maximum number of students in each bus is 46.
Problem 5 :
Charles is saving $5 each week. He earns an extra $15 by mowing his neighbor's lawn. How many weeks will he need to save in order to have at least $75?
a) Write an inequality to represent the situation. Be sure to define your variable.
b) Solve the inequality and answer the question.
Solution :
At least 75 means, more than 75 is also possible.
Let x be the number of weeks he is saving.
5x + 15 ≥ 75
5x ≥ 75 - 15
5x ≥ 60
x ≥ 60/5
x ≥ 12
So, he will need to save 12 weeks.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM