Question 5 of 19intermediate🔧 ApplyNumerical3 marks

I am a 3-digit number. My hundred's digit is 3 less than my ten's digit. My ten's digit is 3 less than my unit's digit. The sum of all the three digits is 15. Who am I?

Correct Answer

Given: Let units digit = uu Tens digit = u−3u - 3 Hundreds digit = u−6u - 6 Sum of all digits = 15

Solution: Step 1: Let units digit = uu. Then tens digit = u−3u - 3 and hundreds digit = u−6u - 6. Step 2: Sum of digits: (u−6)+(u−3)+u=15(u - 6) + (u - 3) + u = 15 Step 3: Simplify: 3u−9=153u - 9 = 15 Step 4: Add 9: 3u=243u = 24 Step 5: Divide by 3: u=8u = 8 Step 6: Tens digit = 8−3=58 - 3 = 5, Hundreds digit = 5−3=25 - 3 = 2 Step 7: The number is 258

Verification: Hundreds digit = 2, Tens digit = 5, Units digit = 8 Each digit is 3 more than the digit to its left 2+5+8=152 + 5 + 8 = 15 ✓

Answer: ∴ The number is 258.

Exercise: Figure it Out (Section 2) | Q: 3 | (Page Page 17)
For More Understanding

Explanation

Let the units digit be uu. Then the tens digit is u−3u - 3 and the hundreds digit is (u−3)−3=u−6(u - 3) - 3 = u - 6. The sum of digits is (u−6)+(u−3)+u=15(u - 6) + (u - 3) + u = 15, giving 3u−9=153u - 9 = 15, so 3u=243u = 24 and u=8u = 8. Therefore, tens digit = 8−3=58 - 3 = 5 and hundreds digit = 5−3=25 - 3 = 2. The number is 258.

Solution Steps

  1. Step 1: Let units digit = uu. Then tens digit = u−3u - 3 and hundreds digit = u−6u - 6.

  2. Step 2: Sum of digits: (u−6)+(u−3)+u=15(u - 6) + (u - 3) + u = 15

  3. Step 3: Simplify: 3u−9=153u - 9 = 15

  4. Step 4: Add 9: 3u=243u = 24

  5. Step 5: Divide by 3: u=8u = 8

  6. Step 6: Tens digit = 8−3=58 - 3 = 5, Hundreds digit = 5−3=25 - 3 = 2

  7. Step 7: The number is 258

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