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Sania plays a game in which she pops balloons and slices fruits.
Let 
B represent the number of points Sania must score by popping balloons and 
F represent the number of points she must score by slicing fruits in order to win the game.

7B+13 F > 650
Sania pops 30 balloons in the game. What is the least number of fruits she must slice to reach her goal?
Choose 1 answer:
(A) Sania must slice at least 13 fruits.
(B) Sania must slice at least 30 fruits.
(c) Sania must slice at least 33 fruits.
(D) Sania must slice at least 34 fruits.

Sania plays a game in which she pops balloons and slices fruits.\newlineLet \newlineB B represent the number of points Sania must score by popping balloons and \newlineF F represent the number of points she must score by slicing fruits in order to win the game.\newline 7B + 13F > 650 \newlineSania pops 30 30 balloons in the game. What is the least number of fruits she must slice to reach her goal?\newlineChoose 11 answer:\newline(A) Sania must slice at least 13 13 fruits.\newline(B) Sania must slice at least 30 30 fruits.\newline(C) Sania must slice at least 33 33 fruits.\newline(D) Sania must slice at least 34 34 fruits.

Full solution

Q. Sania plays a game in which she pops balloons and slices fruits.\newlineLet \newlineB B represent the number of points Sania must score by popping balloons and \newlineF F represent the number of points she must score by slicing fruits in order to win the game.\newline7B+13F>650 7B + 13F > 650 \newlineSania pops 30 30 balloons in the game. What is the least number of fruits she must slice to reach her goal?\newlineChoose 11 answer:\newline(A) Sania must slice at least 13 13 fruits.\newline(B) Sania must slice at least 30 30 fruits.\newline(C) Sania must slice at least 33 33 fruits.\newline(D) Sania must slice at least 34 34 fruits.
  1. Substitute balloons into inequality: Substitute the number of balloons popped into the inequality.\newlineWe know that Sania pops 3030 balloons, so we substitute B=30B = 30 into the inequality 7B + 13F > 650.\newline7(30) + 13F > 650\newline210 + 13F > 650
  2. Solve for F: Solve for F.\newlineTo find the least number of fruits Sania must slice, we need to isolate FF.\newline13F > 650 - 210\newline13F > 440
  3. Divide both sides by 1313: Divide both sides by 1313 to solve for FF.\newlineF > \frac{440}{13}\newlineF > 33.8461538\newlineSince Sania can't slice a fraction of a fruit, she must slice at least the next whole number of fruits, which is 3434.
  4. Choose the correct answer: Choose the correct answer.\newlineSania must slice at least 3434 fruits to reach her goal, which corresponds to answer (D).

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