Learn this concept that can help score AL1 in Math PSLE (Repeated Identity)

Not all tough problem sums involve fractions. Here is an example of a challenging problem that does not use fractions:

Evan, Farah and Gina baked cookies for a school fundraiser.
Evan and Farah baked 112 cookies altogether.
Evan and Gina baked 86 cookies altogether.
Farah and Gina baked 94 cookies altogether.
How many cookies did Farah bake?

What is a Repeated Identity Concept Question?

A Repeated Identity concept question is a type of word problem where the same person or item appears in pairs or in groups.

For example:

Evan and Farah baked 112 cookies
Evan and Gina baked 86 cookies
Farah and Gina baked 94 cookies

Notice how each person appears twice in different pairs. This is the key thing of a repeated identity problem.

How to Spot a Repeated Identity Concept Question

You can tell it's a Repeated Identity concept question when you see:

The same people or items appearing in different groups
Total amounts given for each group or pair
Each person or item appears more than once in the different groups
You need to find the individual amount for one person or item

If each person or thing shows up in at least two different combinations, it's probably a Repeated Identity problem.

Example Question

Problem: Evan, Farah and Gina baked cookies for a school fundraiser. Evan and Farah baked 112 cookies altogether. Evan and Gina baked 86 cookies altogether. Farah and Gina baked 94 cookies altogether. How many cookies did Farah bake?

How to Solve Them

Follow these steps to solve Repeated Identity problems:

Step 1: Write Down What You Know

Use letters to represent each person or item, then write equations for each group.

For the cookies problem:

Let E = Evan's cookies
Let F = Farah's cookies
Let G = Gina's cookies

Write the equations:

E + F = 112
E + G = 86
F + G = 94

Step 2: Add Two Equations Together

Pick two equations that include the person you're looking for. Add them together.

We want to find F (Farah), so let's add the first two equations:

E + F = 112
F + G = 94
Add them: (E + F) + (F + G) = 112 + 94 = 206

This gives us:

E + F + F + G = 206
E + 2F + G = 206

Step 3: Subtract the Remaining Equation

Now subtract the third equation from your result.

We have: E + 2F + G = 206
Subtract: E + G = 86

206 - 86 = 120

This gives us: 2F = 120

Step 4: Solve for the Answer

Divide to find the individual value:

2F = 120
F = 120 ÷ 2
F = 60

Farah baked 60 cookies.

Check Your Answer

Let's verify our answer works:

If F = 60, and E + F = 112, then E = 52
If E = 52, and E + G = 86, then G = 34
Check: F + G = 60 + 34 = 94 ✓

All three equations work!

Tips to Remember

Use letters to represent each person or item - This makes the problem easier to see
Write all the equations first - Don't try to solve in your head
Add the two equations that include what you're looking for - This creates a useful pattern
The answer will always need one more step - You'll get "2 times" the answer, so remember to divide by 2
Always check your answer - Put your numbers back into all the original equations

Why Does This Work?

When you add two equations together, the person you're looking for appears twice, while the others appear only once.

When you subtract the third equation, you remove the people who appear once, leaving you with twice the amount for the person you want to find.

That's why the final step is always dividing by 2!