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Philip is downloading applications (apps) and songs to his tablet. He downloads 7 apps and 6 songs. Each song takes an average of 0.8 minutes longer to download than each app. If it takes 21.7 minutes for his downloads to finish, which of the following systems could be used to approximate
a, the average number of minutes it takes to download one app, and
s, the average number of minutes it takes to download one song?
Choose 1 answer:
(A)
a+s=21.7

6s=7a-0.8
(B)
a+s=21.7

7a=6s-0.8
(C)
7a+6s=21.7

s=a-0.8
(D)
7a+6s=21.7

a=s-0.8

Philip is downloading applications (apps) and songs to his tablet. He downloads $7$ apps and $6$ songs. Each song takes an average of $0$ . $8$ minutes longer to download than each app. If it takes $21$ . $7$ minutes for his downloads to finish, which of the following systems could be used to approximate $a$ , the average number of minutes it takes to download one app, and $s$ , the average number of minutes it takes to download one song? $\newline$ Choose $1$ answer: $\newline$ (A) $a+s=21.7$ $\newline$ $6 s=7 a-0.8$ $\newline$ (B) $a+s=21.7$ $\newline$ $7 a=6 s-0.8$ $\newline$ (C) $7 a+6 s=21.7$ $\newline$ $s=a-0.8$ $\newline$ (D) $7 a+6 s=21.7$ $\newline$ $a=s-0.8$

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Solve linear equations with variables on both sides: word problems

Full solution

Q. Philip is downloading applications (apps) and songs to his tablet. He downloads

7

apps and

6

songs. Each song takes an average of

0

.

8

minutes longer to download than each app. If it takes

21

.

7

minutes for his downloads to finish, which of the following systems could be used to approximate

a

, the average number of minutes it takes to download one app, and

s

, the average number of minutes it takes to download one song?

\newline

Choose

1

answer:

\newline

(A)

a+s=21.7

\newline

6 s=7 a-0.8

\newline

(B)

a+s=21.7

\newline

7 a=6 s-0.8

\newline

(C)

7 a+6 s=21.7

\newline

s=a-0.8

\newline

(D)

7 a+6 s=21.7

\newline

a=s-0.8

Set Up Equations: Step $1$ : Let's set up the equations based on the total time it took for all downloads. We know Philip downloaded $7$ apps and $6$ songs, and it took $21.7$ minutes in total. So the equation is: $\newline$ $7a + 6s = 21.7$
Second Equation: Step $2$ : Now, we need to set up the second equation based on the time difference between downloading a song and an app. Each song takes $0.8$ minutes longer than an app, so: $\newline$ $s = a + 0.8$
Choose Correct System: Step $3$ : We need to choose the correct system of equations from the options given. Let's check each option against our equations from Step $1$ and Step $2$ . $\newline$ Option (A) doesn't match because $a + s = 21.7$ doesn't represent the total time for all downloads. $\newline$ Option (B) doesn't match because $7a = 6s - 0.8$ doesn't represent the relationship between the time it takes to download a song and an app. $\newline$ Option (C) doesn't match because it suggests that $s = a - 0.8$ , which is the opposite of the relationship we established. $\newline$ Option (D) matches our equations: $7a + 6s = 21.7$ represents the total time, and $a = s - 0.8$ represents the relationship between the download times of an app and a song, but with the roles of $a$ and $s$ reversed. We need to correct this to $s = a + 0.8$ .

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