Lana and Emily are playing a competitive word game. Whoever plays all of their tiles first gets to add the value of their word plus the total value of all of their opponent’s remaining tiles to their score. Also, the opponent must subtract the total value of all of their tiles from their score.

Suppose that the current score is: Lana 324, Emily 358. If Lana’s last word is worth 7 points, how many points does she need Emily to have in her hand in order to win?

Suppose that the current score is: Lana 324, Emily 358. If Lana’s last word is worth 7 points, how many points does she need Emily to have in her hand in order to win? ___________ points

Hint: If Emily had 5 points in her hand, by how much would the difference between the player’s scores change?

Question

03-01-2016
Mathematics

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Lana and Emily are playing a competitive word game. Whoever plays all of their tiles first gets to add the value of their word plus the total value of all of their opponent’s remaining tiles to their score. Also, the opponent must subtract the total value of all of their tiles from their score.

Suppose that the current score is: Lana 324, Emily 358. If Lana’s last word is worth 7 points, how many points does she need Emily to have in her hand in order to win?

Suppose that the current score is: Lana 324, Emily 358. If Lana’s last word is worth 7 points, how many points does she need Emily to have in her hand in order to win? ___________ points

Hint: If Emily had 5 points in her hand, by how much would the difference between the player’s scores change?

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zs442 zs442 · Answer 1 · 2016-01-03T02:21:56+01:00

Lana gets the 7 points so she ends up with 331. She will then be 358-331=27points behind Emily. She needs to win, so there needs to be 1 more than 27 points of change in the score, or 28 points. Emily's hand value is added to Lana's and also subtracted from Emily's so her hand is worth twice the value as the amount. (If the hand is worth 10 points, it changes the scores by 20 points). Thus, we only need half of the 28 points of change for Lana to win. The answer is 14 points.