We can write two-step inequalities to represent real-world problems by translating the words of the problems into numbers, variables, and operations.
Example 1 :
A mountain climbing team is camped at an altitude of 18,460 feet on Mount Everest. The team wants to reach the 29,029-foot summit within 6 days. Write an inequality to find the average number of feet per day the team must climb to accomplish its objective.
Solution :
Step 1 :
Identify what you are trying to find. This will be the variable in the inequality.
Let d represent the average altitude the team must gain each day.
Step 2 :
Identify important information in the problem that you can use to write an inequality.
starting altitude : 18,460 ft
target altitude: 29,029 ft
Number of days times altitude gained to reach target altitude : 6 · d
Step 3 :
Use words in the problem to tie the information together and write an inequality.
Step 4 :
Hence, the inequality which represents the given situation is
18,460 + 6d ≥ 29,029
Example 2 :
The 45 members of the glee club are trying to raise $6,000 so they can compete in the state championship. They already have $1,240. What inequality can you write to find the amount each member must raise, on average, to meet the goal?
Solution :
Step 1 :
Identify what you are trying to find. This will be the variable in the inequality.
Let x represent the amount that each member must raise on average to meet the goal.
Step 2 :
Identify important information in the problem that you can use to write an inequality.
starting balance : $1240
target balance : $6000
Number of members times amount raised by each member to reach the target balance : 45 · x
Step 3 :
Use words in the problem to tie the information together and write an inequality.
starting balance ($1240)
+
number of members (45)
times
amount raised by each member (x)
≥
target balance ($6000)
Step 4 :
Hence, the inequality which represents the given situation is
1240 + 45x ≥ 6000
Example 3 :
Ella has $40 to spend at the State Fair. Admission is $6 and each ride costs $3. Write an inequality to find the greatest number of rides she can go on.
Solution :
Step 1 :
Identify what you are trying to find. This will be the variable in the inequality.
Let x represent the total number of rides she can go on.
Step 2 :
Identify important information in the problem that you can use to write an inequality.
admission : $6
cost of each ride : $3
maximum money can be spent : $40
Number of rides times cost per ride to reach the maximum money which can be spent : 3 · x
Step 3 :
Use words in the problem to tie the information together and write an inequality.
admission ($6)
+
aost of each ride ($3)
times
no. of rides (x)
≤
maximum money can be spent ($40)
Step 4 :
Hence, the inequality which represents the given situation is
6 + 3x ≤ 40
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