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.
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:
Final step to answer the question being asked:
Final answer written as a sentence:
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:
Final step to answer the question being asked:
Final answer written as a sentence: