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.
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
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
Trigonometry 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
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