# INTERPRETING WORD PROBLEMS

When we trying to solve word problems involving real numbers, we often need to think about the problem to decide which operations to be used.

Let us see how to interpret word problems.

We have to do the following steps to interpret a word problem.

Step 1 :

Analyze Information

Step 2 :

Formulate a Plan

Step 3 :

Solve

Step 4 :

Justify and Evaluate

## Examples

Examples 1 :

Lily earned \$54 mowing lawns in two days. She worked 2.5 hours yesterday and 4.25 hours today. If Naomi was paid the same amount for every hour she works, how much did she earn per hour ?

Solution :

Analyze Information :

Identify the important information.

• Naomi made \$54 mowing lawns.

• Naomi worked 2.5 hours yesterday and 4.25 hours today.

• We are asked to find how much she earned per hour

Formulate a plan :

• The total amount she earned divided by the total hours she worked gives the amount she earns per hour.

• Use the expression 54 ÷ (2.5 + 4.25) to find the amount she earned per hour.

Solve :

(2.5 + 4.25)  =  6.75  ---- > (Add inside parentheses)

54 ÷ 6.75  =  8 ---- > (Divide)

Lily earned \$8 per hour mowing lawns.

Justify and Evaluate :

We have added 2.5 and 4.25 first to find the total number of hours worked.

Then, we have divided 54 by the sum to find the amount earned per hour.

Examples 2 :

David traveled from A to B in 3 hours at the rate of 50 miles per hour. Then he traveled from B to C in 2 hours at the rate of 60 miles per hour. What is the average speed of David from A to C ?

Solution :

Analyze Information :

Identify the important information.

• David traveled from A to B in 3 hours @ 50 mph.

• David traveled from B to C in 2 hours @ 60 mph.

• We are asked to find the average speed from A to C.

Formulate a plan :

• The total distance covered from A to C divided by total time taken gives the average speed from A to C.

• Use the expression (3 x 50) + (2 x 60)  to find the total distance from A to C.

That is, 270 miles

• Use the expression (3 + 2)  to find the total time taken from A to C.

That is, 5 hours

Solve :

Divide the total distance (A to C) by the total time taken (A to C)

270 ÷ 5  =  54 ---- > (Divide)

Hence, the average speed from A to C is 54 miles per hour.

Justify and Evaluate :

We have multiplied time and speed to find the distance.

Then, we have divided the total distance covered by total time taken to find the average speed.

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

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6