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Eliana takes photos and videos on her phone.
Let
P represent the number of photos and
V represent the number of videos that Eliana can take using her storage space.

15 P+70 V < 400
Eliana wants to take 12 photos. How many videos at most can she take with the remaining storage space?
Choose 1 answer:
(A) Eliana can take at most 3 videos.
(B) Eliana can take at most 4 videos.
(c) Eliana can take at most 12 videos.
(D) Eliana can take at most 15 videos.

Eliana takes photos and videos on her phone. $\newline$ Let $P$ represent the number of photos and $V$ represent the number of videos that Eliana can take using her storage space. $\newline$ $15P + 70V < 400$ $\newline$ Eliana wants to take $12$ photos. How many videos at most can she take with the remaining storage space? $\newline$ Choose $1$ answer: $\newline$ (A) Eliana can take at most $3$ videos. $\newline$ (B) Eliana can take at most $4$ videos. $\newline$ (C) Eliana can take at most $12$ videos. $\newline$ (D) Eliana can take at most $15$ videos.

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Modeling with linear inequalities

Full solution

Q. Eliana takes photos and videos on her phone.

\newline

Let

P

represent the number of photos and

V

represent the number of videos that Eliana can take using her storage space.

\newline

15P + 70V < 400

\newline

Eliana wants to take

12

photos. How many videos at most can she take with the remaining storage space?

\newline

Choose

1

answer:

\newline

(A) Eliana can take at most

3

videos.

\newline

(B) Eliana can take at most

4

videos.

\newline

(C) Eliana can take at most

12

videos.

\newline

(D) Eliana can take at most

15

videos.

Substitute and simplify: Substitute the number of photos into the inequality. $\newline$ Given the inequality $15P + 70V < 400$ and knowing that Eliana wants to take $12$ photos, we substitute $P$ with $12$ . $\newline$ $15(12) + 70V < 400$
Calculate storage space for photos: Perform the multiplication to find out how much storage space the photos will take. $\newline$ $15 \times 12 = 180$ $\newline$ So, $180 + 70V < 400$
Calculate storage space for videos: Subtract the storage space used by the photos from the total storage space to find out how much storage is left for videos. $\newline$ $400 - 180 = 220$ $\newline$ So, $70V < 220$
Solve for V: Divide the inequality by $70$ to solve for $V$ . $\newline$ $V < \frac{220}{70}$ $\newline$ $V < 3.14285714$
Round down to whole number: Since $V$ must be a whole number (as Eliana cannot take a fraction of a video), we round down to the nearest whole number. $\newline$ Eliana can take at most $3$ videos.

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