CEMC Fermat

Algebra Difficulty 2.4 Junior Find the answer

Fifty numbers have an average of 76. Forty of these numbers have an average of 80. What is the average of the other ten numbers?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

If 50 numbers have an average of 76, then the sum of these 50 numbers is $50(76)=3800$ . If 40 numbers have an average of 80, then the sum of these 40 numbers is $40(80)=3200$ . Therefore, the sum of the 10 remaining numbers is $3800-3200=600$ , and so the average of the 10 remaining numbers is $\frac{600}{10}=60$ .

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