Sania plays a game in which she pops balloons and slices fruits.

Question

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

Answer 1

To determine the least number of fruits Sania must slice to reach her goal, let's first calculate the points she earns from popping 30 balloons.

Each balloon popped gives Sania 7 points. Therefore, if she pops 30 balloons, the total points from popping balloons is:

\[ B = 30 \quad \text{(number of balloons)} \] \[ \text{Points from balloons} = 7B = 7 \times 30 = 210 \]

Now, the total points she needs to exceed is given by the inequality:

\[ 7B + 13F > 650 \]

Substituting the points from popping balloons into the equation, we have:

\[ 210 + 13F > 650 \]

To isolate \(F\), subtract 210 from both sides:

\[ 13F > 650 - 210 \] \[ 13F > 440 \]

Now, divide both sides by 13 to solve for \(F\):

\[ F > \frac{440}{13} \approx 33.846 \]

Since \(F\) must be a whole number, we take the next whole number greater than 33.846, which is 34. Thus, Sania must slice at least 34 fruits.

Hence, the correct answer is:

(Choice D) Sania must slice at least 34 fruits.