# Mixed Operations Word Problems (3-step word problems)

In these lessons we look at examples of word problems with mixed operations that can be solved in three or more steps. We will illustrate how block diagrams can be used to help you to visualize the word problems in terms of the information given and the data that needs to be found. Block diagrams or block modeling are used in Singapore Math. Block diagrams are also called Tape Diagrams in Common Core.

Example:
There were 42 mangoes in each crate. 12 such crates of mangoes were delivered to a factory. 4 mangoes were rotten and had to be thrown away. The remaining mangoes were packed into boxes of 10 mangoes each. How many boxes of mangoes were there?

Solution:
Step 1: Find the total number of mangoes delivered. 12 × 42 = 504
The total number of mangoes delivered was 504.

Step 2: Find the number of remaining mangoes. 504 – 4 = 500

Step 3: Find the number of boxes of mangoes. 500 ÷ 10 = 50
There were 50 boxes of mangoes.

Example:
There were 9500 spectators at a football match. 6375 of them were men. Of the remaining spectators, there were 4 times as many children as women. How many children were there?

Solution:
Step 1: Find the number of women and children. 9500 – 6375 = 3125

There were 3125 women and children.

Step 2: Find the number of women. 3125 ÷ 5 = 625
There were 625 women.

Step 3: Find the number of children. 625 × 4 = 2500
There were 2500 children.

How to use bar models to solve a word problem that involves “three times as many” and “4 more”?

Example:
Claire loves animals. She has three times as many goldfish as she has chickens. She has four more hamsters than chickens. Altogether, she has 49 animals (just goldfish, hamsters and chickens). How many more goldfish does she have than hamsters?

How to solve a problem involving “8 less than twice as many.”?

Example:
Steve collects baseball cards. He has 8 fewer than twice as many Padres cards as Giants cards. He has three times as many Dodgers cards as Giants cards. Altogether, he has 82 cards. How many Padres cards does he have?

Visual Problem Solving - Singapore Style

Example:
2 tablets and 4 mini-tablets cost a total of \$2,480. A tablet and a mini-tablet cost \$870 all together. How much does a mini-tablet cost?

A model drawing involving multiples is used to solve a complex word problem

Example:
Billy, Robert, and DJ had 210 model cars. Billy had twice as many cars as Robert. Robert had 3 times as many models as DJ. How many model cars did Billy have?

How to use a Singapore style model drawing involving fractions to solve a complex story problem?

Example:
At the school talent show, 1/3 of the people were boys, 3/6 were girls, and the rest were adults. If there were 50 more girls than adults, how many people were there in total?

Example:
Bernardo is 5 times older than Irma. Irma is five years older than Oswaldo. If the sum of their ages is 65 years, how old will Oswaldo be in 7 years?

Visual problem solving using Singapore methods via model drawing which includes multiples, division, subtraction, and logical reasoning

Example:
Cameron scored 5 times as many points as Lars in a basketball game. Mike scored an amount equal to the 6th multiple of 9. If the 3 boys scored a total of 126 points, how many points did Cameron score?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 