Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.8 Junior Find the answer

Lauren plays basketball with her friends. She makes 10 baskets. Each of these baskets is worth either 2 or 3 points. Lauren scores a total of 26 points. How many 3 point baskets did she make?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Suppose that Lauren makes $x$ baskets worth 3 points each. Since she makes 10 baskets, then $10-x$ baskets that she made are worth 2 points each. Since Lauren scores 26 points, then $3 x+2(10-x)=26$ and so $3 x+20-x=26$ which gives $x=6$ . Therefore, Lauren makes 6 baskets worth 3 points.

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