Problem 21 · 2023 Math Kangaroo
Stretch
Arithmetic & Operations
sum-constraint
Adam has 9 marbles and Brenda also has 9 marbles. Together they have 8 white and 10 black marbles. Brenda has twice as many black marbles as white marbles. How many black marbles does Adam have?
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Answer: B — 4
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Hint 1 of 2
Brenda has 9 marbles, and her black pile is twice as big as her white pile.
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Hint 2 of 2
Once you know how many black marbles Brenda has, the rest of the 10 black ones must be Adam's.
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Approach: split Brenda's 9 into equal groups, then give the rest of the black marbles to Adam
- Brenda's black pile is twice her white pile, so think of 1 white group and 2 matching black groups: that is 3 equal groups making 9, so each group is 3.
- Brenda then has 3 white and 6 black marbles.
- There are 10 black marbles altogether, so Adam has the leftover 10 − 6 = 4 black marbles.
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