Sure! We'll solve the inequality step-by-step to find the least number of fruits \( F \) Sania must slice to score more than 650 points, given that she pops 30 balloons.
Given the inequality:
[tex]\[ 7B + 13F > 650 \][/tex]
We know Sania pops \( B = 30 \) balloons. Let's substitute \( B \) with 30 in the inequality:
[tex]\[ 7(30) + 13F > 650 \][/tex]
First, compute the points from popping the balloons:
[tex]\[ 7 \cdot 30 = 210 \][/tex]
Now, substitute this into the inequality:
[tex]\[ 210 + 13F > 650 \][/tex]
Next, isolate the term involving \( F \) by subtracting 210 from both sides of the inequality:
[tex]\[ 13F > 650 - 210 \][/tex]
[tex]\[ 13F > 440 \][/tex]
To find \( F \), divide both sides of the inequality by 13:
[tex]\[ F > \frac{440}{13} \][/tex]
Calculate the right-hand side:
[tex]\[ F > 33.846 \][/tex]
Since \( F \) must be an integer (as you can't slice a fraction of a fruit in the context of the game), we need to round up to the next whole number:
[tex]\[ F = \lceil 33.846 \rceil \][/tex]
[tex]\[ F = 34 \][/tex]
So, the least number of fruits Sania must slice to reach her goal of scoring more than 650 points is [tex]\( \boxed{34} \)[/tex].
