Problem 28 · 2018 Math Kangaroo
Stretch
Arithmetic & Operations
total-then-divide
Viola practices long-jumping. On average she has jumped 3.80 m so far. On her next jump she reaches 3.99 m and thus her mean increases to 3.81 m. How far does she have to jump on her next attempt in order to increase her mean to 3.82 m?
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Answer: C — 4.01 m
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Hint 1 of 2
First use the jump from 3.80 to 3.81 average to find how many jumps she had.
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Hint 2 of 2
Then work out the new total she needs for a 3.82 average and subtract.
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Approach: find the count of jumps, then the required total
- If the mean rises from 3.80 to 3.81 after a 3.99 m jump, then 3.80n + 3.99 = 3.81(n+1), giving n = 18 (now 19 jumps, total 72.39 m).
- For a mean of 3.82 over 20 jumps the total must be 76.40 m.
- So the next jump must be 76.40 − 72.39 = 4.01 m.
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