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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, [tex] B [/tex] represents the number of balloons Sania pops and [tex] F [/tex] represents the number of fruits she slices:

[tex]\[ 7B + 13F \ \textgreater \ 650 \][/tex]

If Sania pops 30 balloons in the game, what is the least number of fruits she must slice to reach her goal?



Answer :

GinnyAnswer
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].

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