Problem 18 · 2016 Math Kangaroo
Stretch
Arithmetic & Operations
sum-constraintages
Tick, Trick and Track are triplets. Their brother Franz is exactly 3 years older. All four children are having their birthdays today. How old can the four brothers be altogether?
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Answer: B — 27
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Hint 1 of 2
The three triplets are all the same age, and Franz is just 3 more than that.
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Hint 2 of 2
If you take Franz's extra 3 years off the total, what is left should split into four equal ages.
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Approach: take off Franz's extra 3, then split the rest into four equal ages
- All four boys would be the same age except Franz, who has 3 extra years, so take those 3 away from the total first.
- What is left must split evenly into four equal ages (one for each boy).
- Take 3 off each choice and see which splits into 4 equal whole numbers: 27 − 3 = 24, and 24 shared by 4 is 6 each, so the ages are 6, 6, 6 and 9.
- So the four brothers can be 27 years old altogether, choice B.
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