Solving Word Problems

Here are some examples of mixed operations word problems. These problems are slightly more challenging, but they also illustrate how helpful the block diagrams can be. The block diagrams are used to help solve word problems that would usually require algebra.

Example:

Two bowls and three plates cost $1421. The cost of the plate is half the cost of the bowl. What is the cost of the bowl?

Solution:

Step 1; Draw a block diagram to illustrate the number of bowls and plates. (In this diagram, the bowls are shown as orange blocks and the plates as blue blocks.)

Step 2: Since a bowl costs twice as much as a plate, we can replace one orange block (bowl) with two blue blocks (plate).

Step 3: Looking at the block diagram, find the cost of each plate.

7 blue blocks = 1421

1 blue block = 1421 ÷ 7 = 203

The cost of each plate is $203.

The cost of each bowl is 203 × 2 = $406.

Example:

A factory makes 4250 bars of chocolate. There were three kinds of chocolate bars – creamy, milky and white. The number of white chocolate bars was 715 more than the number of milky chocolate bars. The number of creamy chocolate bars was 5 times the number of milky chocolate bars. How many creamy chocolate bars did the factory make?

Solution:

Step 1; Draw a block diagram to illustrate the different types of chocolate bars. (In this diagram, the creamy chocolate bars are shown as orange blocks, the milky chocolate bars as blue blocks and the white chocolate bars as red blocks.)

Step 2: Since the number of creamy chocolate bars was 5 times the number of milky chocolate bars, we can replace one orange block (creamy) with 5 blue blocks (milky).

Since the number of white chocolate bars was 715 more than the number of milky chocolate bars, we replace one red block with one blue block + 715.

Step 3: Looking at the block diagram, find the number of milky chocolate bars (blue block)

4250 – 715 = 3535

7 blue blocks = 3535

1 blue block = 3535 ÷ 7 = 505

The number of milky chocolate bars made was 505.

Step 4: Calculate the number of creamy chocolate bars.

The number of creamy chocolate bars was 5 times the number of milky chocolate bars = 5 × 505 = 2525

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