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 : 

Follow the order of operations.

(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. 

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