Math Strategies Explained: Same Identity & Unchanged Variable

In the previous article, I have shown you two strategies on Same Difference and Same Total. Today, I will continue to share with you two more key strategies that are often tested in school-based examinations or PSLE Math – Same Identity and Unchanged Variable.

Key Strategy 3: Same Identity

The MRT broke down in the evening when Alan, Betty and Clive wanted to go home from work. They shared the cost of “grabbing” a private hire car. Alan paid $\frac{5}{6}$ the amount paid by Betty and Clive. The amount paid by Betty to Clive is in the ratio 5 : 4. If Alan paid $20 more than Betty, how much was the cost of “grabbing” the private hire car?

1) Study and Understand the Problem

There are three variables in the problem sums – Alan, Betty and Clive.

Alan paid $\frac{5}{6}$ the amount paid by Betty and Clive. This can be restated in ratio as A : B&C = 5 : 6

The amount paid by Betty to Clive is in the ratio 5 : 4.

2) Think of a Plan

Contextual clue: The variables, Betty and Clive, appear in both sets of ratios and the amount paid by each of them remained the same too in both sets of ratios.

When we see same identity of variable in both sets of ratios without any change in value represented by the same identity, we can use the strategy “Same Identity”.

3) Act on the Plan

There is the same identity of B and C in the two sets of ratios, thus make the total number of units for B and C for both sets of ratios the same.

5 units = $20
1 unit = $4
15 units + 10 units + 8 units = 33 units
33 units = 33 × $4 = $132

4) Reflect on my Answer

Work your answer through the steps to double check on accuracy.

15 units = $60 (A)
10 units = $40 (B)
8 units = $32 (C)

A : B + C
60 : 72
5 : 6 (correct!)

B : C
40 : 32
5 : 4 (correct!)

Key Strategy 4 : Unchanged Variable

The ratio of the number of students in the Dance Club to the number of students in the Choir was 5 : 7. After 22 students left the Dance Club, the ratio became 2 : 5. Find the number of students in the Choir.

1) Study and Understand the Problem

There are two variables in the questions – Dance Club and Choir
22 students left the Dance Club.
The number of students in Choir remained the same for “Before” and “After” scenarios.

2) Think of a Plan

Contextual clue: The number of students in choir remained the same for “Before” and “After” scenarios.

Whenever one of the variables remained the same for “Before” and “After” scenarios, you can use the strategy of “Unchanged variable”.

3) Act on the Plan

Strategy: Since there was no change in the number of students from Choir, the number of units representing choir should be the same.

Decrease → 25 units – 14 units = 11 units
11 units = 22
1 unit = 2

Total number of students in Choir → 35 units

35 units = 70

4) Reflect on my Answer

Work your answer through the steps to double check on accuracy.

Conclusion

Problem sums that can be solved using the strategies of Same Identity and Unchanged Variable are frequently tested in Math exam papers. Subscribe to OwlSmart and gain access to more than 50 questions designed to be solved using the 2 strategies shared here.