MODELING PERCENT PROBLEMS

In this section, you will learn how to solve real world problems involving percent using model. 

Let us see how models can be used too solve percent problems.

Example :

A sports store received a shipment of 400 baseball gloves. 30% were left-handed. How many left-handed gloves were in the shipment ?

Question (i) :

Complete the diagram to model this situation.

Answer :

Question (ii) :

What does 30% mean ?

Answer :

30 % means 30 out of 100. 

Question (iii) :

How many left-handed gloves were there for every 100 baseball gloves ?

Answer :

There were 30 left-handed gloves were there for every 100 baseball gloves.

Question (iv) :

Describe how the diagram models the shipment of gloves.

Answer : 

One large rectangle represents 100 gloves so 4 rectangles represent 400 gloves. One small rectangle represents 30 out of 100 gloves that are left-handed.

Question (v) :

Explain how you can use the diagram to find the total number of left-handed gloves in the shipment.

Answer : 

There were 30 left-handed gloves in each 100 baseball gloves. 

To find the total number of left handed gloves, we have to add the 30s in all the four parts. 

So, we have 

30 + 30 + 30 + 30  =  120

Question (vi) :

Use a bar model to solve this problem. The bar represents 100%, or the entire shipment of 400 gloves. The bar is divided into 10 equal parts. Complete the labels along the bottom of the bar.

Answer :

Question (vii) :

How did you determine the labels along the bottom of the bar model in question (v) ?

Answer :

The bar shows 400 divided into 10 equal parts, so each part represents 400 ÷ 10 = 40.

That is, for every 10% increase at the top, there is an increase of 40 at the bottom.

Based on this fact, we can complete the labels along the bottom of the bar

0%  =  0

10%  =  40 <--------(0 + 40)

20%  =  80 <--------(40 + 40)

30%  =  120 <--------(80 + 40)

40%  =  160 <--------(120 + 40)

50%  =  200 <--------(160 + 40)

60%  =  240 <--------(200 + 40)

70%  =  280 <--------(240 + 40)

80%  =  320 <--------(280 + 40)

90%  =  360 <--------(320 + 40)

100%  =  400 <--------(360 + 40)

Question (viii) :

How can you use the bar model to find the number of left-handed gloves ?

Answer :

30% of 400  =  (30/100) x 400

30% of 400  =  30 x 4

30% of 400  =  120

There were 120 left-handed gloves.

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