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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. $\newline$ Let $\newline$ $B$ represent the number of points Sania must score by popping balloons and $\newline$ $F$ represent the number of points she must score by slicing fruits in order to win the game. $\newline$ $7B + 13F > 650$ $\newline$ Sania pops $30$ balloons in the game. What is the least number of fruits she must slice to reach her goal? $\newline$ Choose $1$ answer: $\newline$ (A) Sania must slice at least $13$ fruits. $\newline$ (B) Sania must slice at least $30$ fruits. $\newline$ (C) Sania must slice at least $33$ fruits. $\newline$ (D) Sania must slice at least $34$ fruits.

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Modeling with linear inequalities

Full solution

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

\newline

Let

\newline

B

represent the number of points Sania must score by popping balloons and

\newline

F

represent the number of points she must score by slicing fruits in order to win the game.

\newline

7B + 13F > 650

\newline

Sania pops

30

balloons in the game. What is the least number of fruits she must slice to reach her goal?

\newline

Choose

1

answer:

\newline

(A) Sania must slice at least

13

fruits.

\newline

(B) Sania must slice at least

30

fruits.

\newline

(C) Sania must slice at least

33

fruits.

\newline

(D) Sania must slice at least

34

fruits.

Substitute balloons into inequality: Substitute the number of balloons popped into the inequality. $\newline$ We know that Sania pops $30$ balloons, so we substitute $B = 30$ into the inequality $7B + 13F > 650$ . $\newline$ $7(30) + 13F > 650$ $\newline$ $210 + 13F > 650$
Solve for F: Solve for F. $\newline$ To find the least number of fruits Sania must slice, we need to isolate $F$ . $\newline$ $13F > 650 - 210$ $\newline$ $13F > 440$
Divide both sides by $13$ : Divide both sides by $13$ to solve for $F$ . $\newline$ $F > \frac{440}{13}$ $\newline$ $F > 33.8461538$ $\newline$ Since Sania can't slice a fraction of a fruit, she must slice at least the next whole number of fruits, which is $34$ .
Choose the correct answer: Choose the correct answer. $\newline$ Sania must slice at least $34$ fruits to reach her goal, which corresponds to answer (D).

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