Don't Use Guess and Check, Use This Method Instead: Assumption

When students sees a question that can be solved using guess and check – they will trying different numbers until something works. But here's the problem: students who use guess and check are wasting precious time, especially during exams when every minute counts.

Why Guess and Check Wastes Time

Let's see what happens when students use guess and check on a typical problem sum:

A jar has 42 coins (20¢ and 50¢) worth $14.40. How many 20¢ coins?

Student Using Guess and Check:

Attempt 1: "Maybe 20 twenty-cent coins?"

• 20 × $0.20 = $4.00
• 22 × $0.50 = $11.00
• Total = $15.00 ❌ Too high!

Attempt 2: "Maybe 25 twenty-cent coins?"

• 25 × $0.20 = $5.00
• 17 × $0.50 = $8.50
• Total = $13.50 ❌ Too low!

Attempt 3: "Maybe 22 twenty-cent coins?"

• 22 × $0.20 = $4.40
• 20 × $0.50 = $10.00
• Total = $14.40 ✓ Finally!

Time wasted: it can go up to 20 to 30 minutes with multiple calculations and careless mistakes. Yes, I have student who took that long.

Therefore, there is a better way: Assumption method. I'll show you exactly how to identify assumption concept problems and solve them using a reliable 4-step method that will save you time and eliminate errors.

How to Spot Assumption Problem Sum Question

Look for these THREE things:

1. Total number of items: The question tells you how many items there are in total (e.g., "42 coins in total")

2. Total sum/value of items: The question tells you the combined value of all items (e.g., "$14.40 altogether")

3. Two different items with different values: There are exactly two types of items, each with its own value (e.g., "20-cent coins or 50-cent coins")

If you can check all three things, you've got an assumption concept problem sum question!

The 4-Step Assumption Method (With Worked Example)

The Question

A donation jar has 42 coins in total, worth $14.40 altogether. The coins are either 20-cent coins or 50-cent coins. How many 20-cent coins are there?

Here's the step by step on how to use Assumption to solve this question:

Step 1: Assume all items are the item that you are not finding.

Example Question: A jar has 42 coins (20¢ and 50¢) worth $14.40. How many 20¢ coins?

What you are finding: 20¢

What you are not finding: 50¢

Therefore, assume all the items are 50¢ coins

Step 2: Calculate the total value of your assumption

If all 42 coins were 50-cent coins:

Total value if we assume all are 50¢ coins

= 42 × $0.50 = $21.00

Step 3: Find 2 differences

1. Difference between your assumed total and the actual total
   Assumed total = $21.00
   Actual total = $14.40
   Difference = $21.00 - $14.40 = $6.60
2. Difference between the values of the two item types
   50-cent coin = $0.50
   20-cent coin = $0.20
   Difference = $0.50 - $0.20 = $0.30

Step 4: Divide the differences to find item you are finding (i.e. 20¢ coins)

Number of 20¢ coins

= Difference between your assumed total and the actual total ÷
Difference between the values of the two item types

= 6.60 ÷ 0.30

= 22

Step 5: Double confirm

Let's check if our answer is correct:

20-cent coins: 22 coins → 22 × $0.20 = $4.40

50-cent coins: 42 - 22 = 20 coins → 20 × $0.50 = $10.00

Total coins: 22 + 20 = 42 coins ✓

Total value: $4.40 + $10.00 = $14.40 ✓

Conclusion

Stop wasting time with guess and check! The Assumption Method is faster, more reliable, and works every single time.

Once you master the 4-step approach – assume the OTHER item, calculate assumed total, find TWO differences, and divide – you'll never go back to guessing again.

Key takeaways:

• ✅ Assumption method saves 3-5 minutes per question
• ✅ Works systematically without any guessing
• ✅ Reduces careless errors
• ✅ Perfect for exam situations where time is precious
• ✅ One method works for all types of mixture problems