AlgebraHardTwo numbers from a sum and a relation
Algebra practice question
The sum of two numbers is 30, and twice the smaller number exceeds the larger number by 3. What is the smaller number?
Answer: 11
Let s and l be the numbers: s + l = 30 and 2s − l = 3. Adding the equations: 3s = 33, so s = 11 (and l = 19). Check: 22 − 19 = 3.
Common wrong answers
- If you answered 9
- 9 comes from 2s − l = −3 (the relation reversed), giving 3s = 27.
- If you answered 15
- 15 is half of 30, treating the numbers as equal.
- If you answered 19
- 19 is the LARGER number.
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