Problem 16 · 2016 Math Kangaroo
Medium
Algebra & Patterns
sum-constraint
Tim, Tom and Jim are triplets. Their twin brothers John and James are 3 years younger. All five have their birthday today. Which of the following numbers could be the sum of the ages of the five brothers?
Show answer
Answer: B — 89
Show hints
Hint 1 of 2
Let the triplets be age t; the twins are t − 3 each. Write the total.
Still stuck? Show hint 2 →
Hint 2 of 2
The sum is 5t − 6, so the answer plus 6 must be a multiple of 5.
Show solution
Approach: express the sum and test the form
- Three triplets are each age t and two twins are each t − 3.
- Total = 3t + 2(t − 3) = 5t − 6, so (sum + 6) must be a multiple of 5.
- 89 + 6 = 95 = 5 × 19 works (t = 19); the other options fail, so the sum can be 89.
Mark:
· log in to save