**Writing two step inequalities :**

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.

After having gone through the stuff given above, we hope that the students would have understood "Writing two step inequalities".

Apart from the stuff given above, if you want to know more about "Writing two step inequalities", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**