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7B+13 F > 650 Sania plays a game in which she pops balloons and slices fruits. She scores 7 points for every balloon she pops and 13 points for every fruit she slices. Sania's goal is to score more than 650 points in the game. In the given inequality, B represents the number of balloons Sania pops and F represents the number of fruits she slices. If Sania pops 30 balloons in the game, what is the least number of fruits she must slice to reach her goal?

7 B+13 F>650 \newlineSania plays a game in which she pops balloons and slices fruits. She scores 77 points for every balloon she pops and 1313 points for every fruit she slices. Sania's goal is to score more than 650650 points in the game. In the given inequality, B B represents the number of balloons Sania pops and F F represents the number of fruits she slices. If Sania pops 3030 balloons in the game, what is the least number of fruits she must slice to reach her goal?

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Q. 7B+13F>650 7 B+13 F>650 \newlineSania plays a game in which she pops balloons and slices fruits. She scores 77 points for every balloon she pops and 1313 points for every fruit she slices. Sania's goal is to score more than 650650 points in the game. In the given inequality, B B represents the number of balloons Sania pops and F F represents the number of fruits she slices. If Sania pops 3030 balloons in the game, what is the least number of fruits she must slice to reach her goal?
  1. Substitute B value: We are given the inequality 7B + 13F > 650, where BB is the number of balloons Sania pops and FF is the number of fruits she slices. We need to find the minimum value of FF when BB is 3030.
  2. Calculate balloons score: First, let's substitute the value of BB (3030 balloons) into the inequality to find the contribution of the balloons to the total score. This gives us 7 \times 30 + 13F > 650.
  3. Isolate term with F: Calculating the score from the balloons, we get 210 + 13F > 650.
  4. Divide by 1313: Next, we subtract 210210 from both sides of the inequality to isolate the term with FF. This gives us 13F > 650 - 210.
  5. Round up to 3434 fruits: Subtracting 210210 from 650650, we get 13F > 440.
  6. Round up to 3434 fruits: Subtracting 210210 from 650650, we get 13F > 440.Now, we divide both sides of the inequality by 1313 to solve for FF. This gives us F > rac{440}{13}.
  7. Round up to 3434 fruits: Subtracting 210210 from 650650, we get 13F > 440. Now, we divide both sides of the inequality by 1313 to solve for FF. This gives us F > \frac{440}{13}. Dividing 440440 by 1313, we get F > 33.8461538462. Since FF represents the number of fruits Sania must slice, and it must be a whole number, we round up to the next whole number because she needs to score more than 650650 points.
  8. Round up to 3434 fruits: Subtracting 210210 from 650650, we get 13F > 440. Now, we divide both sides of the inequality by 1313 to solve for FF. This gives us F > rac{440}{13}. Dividing 440440 by 1313, we get F > 33.8461538462. Since FF represents the number of fruits Sania must slice, and it must be a whole number, we round up to the next whole number because she needs to score more than 650650 points. Rounding up, Sania must slice at least 65065011 fruits to score more than 650650 points.

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