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Multi-Step Word Problems Worksheet: Challenging

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Word Problems Involving Comparison of Numbers
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Reteach: Multi-Step Word Problems (Challenging)

In multi-step word problems, one or more problems have to be solved in order to get the information needed to solve the question being asked. The danger with this type of problem is thinking that you have reached your answer after solving only part of the problem, and stopping too soon.

The problems on this page are intended to be challenging, so be sure to read everything carefully. Before rushing to solve the problem, it is worth your time to slow down and clarify your understanding. Know what is being asked, what is given to you in the problem, and what you need to know in order to solve the question being asked.

Look for information that can be used together (by adding, subtracting, multiplying, or dividing), to provide you with information you need to solve the question you are being asked.

When you finish solving, make sure your answer makes sense.
 

 

Reteach: Guided Practice

Let's look at a challenging multi-step problem:

A salesman bought a case of 48 backpacks for $576. He sold 17 of them for $18 at the swap meet, and the rest were sold to a department store for $25 each. How much was the salesman's profit?

Start by clarifying what you understand, and what you are being asked to solve.

  • 48 is the total number of backpacks.
  • $576 is the amount of money he spent. 
  • 17 is the total sold for $18 each.
  • “The rest” means the number left after the 17 were sold. 48-17 = 31, so 31 is the total sold for $25 each.
  • “How much was the salesman’s profit?” is the question being asked.

17 x $18 = $306 and 31 x $25 = $775. The total he earned was $306 + $775 = $1,081. 

Since profit is money earned minus money spent, his profit is $1,081 - $576 = $505.  The salesman’s profit was $505.

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Independent Practice: Multi-Step Word Problems (Challenging)

Solve the problems below. Check and make sure your answer is reasonable.

A moving company is hired to take 578 clay pots to a florist shop. The florist will pay the moving company a $200 fee, plus $1 for every pot that is delivered safely. The moving company must pay the florist $4 each for any pots that are lost or broken. If two pots are lost, four pots are broken, and the rest are delivered safely, how much should the moving company be paid?

Information I can find by adding, subtracting, multiplying, or dividing the information I'm given:   Number of pots lost/ broken? 4 + 2 = 6; Number of pots delivered safely? 578 - 6 = 572; Fee paid to company $200; Amount paid to company for safely delivered pots? $572 x 1 = $572; Amount company is charged for lost/ broken pots? $4 x 6 = $24; .   

Final step to answer the question being asked:   $200 + $572 - $24 = $748   

Final answer written as a sentence:   The moving company should be paid $748.   

 

The school band is going to a competition. Five members play the flute. There are three times as many members who play the trumpet. There are eight fewer trombone players than trumpeters, and eleven more drummers than trombone players. There are twice as many members that play the clarinet as members that play the flute. There are four fewer tuba players than there are trombone players, but three more members play the French horn than play the trombone. The band director, his assistant, and six parent volunteers are also going. How many seats are needed on the bus?

 

Information I can find by adding, subtracting, multiplying, or dividing the information I’m given:   How many play flute? 5; How many play trumpet? 3 x 5 = 15; How many play trombone? 15 - 8 = 7; How many drummers? 7 + 11 = 18; How many clarinet players? 2 x 5 = 10; How many tuba players? 7 - 4 = 3; How many French Horn players? 7 + 3 = 10; How many other people? 1 + 1 + 6 = 8.   

Final step to answer the question being asked:

  5 + 15 + 7 + 18 + 10 + 3 + 10 + 8 = 76   

Final answer written as a sentence:   76 seats are needed on the bus.   

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A Word Problems Worksheet    -    By HelpingWithMath.com

Related Resources

The various resources listed below are aligned to the same standard, (4OA03) taken from the CCSM (Common Core Standards For Mathematics) as the Word problems Worksheet shown above.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Example/Guidance

Worksheet

Multi-step

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Use the four operations with whole numbers to solve problems