Finn and Gabby are selling raffle tickets for a school fundraiser. If Gabby sold $17$ fewer raffle tickets than Finn did, which of the following represents the relationship between $f$ , the number of tickets Finn sold and $g$ , the number of tickets Gabby sold? $\newline$ Choose $1$ answer: $\newline$ (A) $f+g=17$ $\newline$ (B) $f-g=17$ $\newline$ (C) $f g=17$ $\newline$ (D) $\frac{f}{g}=17$

Full solution

Q. Finn and Gabby are selling raffle tickets for a school fundraiser. If Gabby sold

17

fewer raffle tickets than Finn did, which of the following represents the relationship between

f

, the number of tickets Finn sold and

g

, the number of tickets Gabby sold?

\newline

Choose

1

answer:

\newline

(A)

f+g=17

\newline

(B)

f-g=17

\newline

(C)

f g=17

\newline

(D)

\frac{f}{g}=17

Define Variables: Let's define the variables according to the information given: $\newline$ $f =$ the number of tickets Finn sold $\newline$ $g =$ the number of tickets Gabby sold $\newline$ We are told that Gabby sold $17$ fewer raffle tickets than Finn did. This can be translated into the equation $g = f - 17$ .
Check Given Options: Now let's check each of the given options to see which one correctly represents the relationship $g = f - 17$ .
(A) $f + g = 17$ does not match our equation because it suggests that the sum of the tickets sold by Finn and Gabby is $17$ , which is not what the problem states.
Evaluate Option (A): (B) $f - g = 17$ is the rearranged form of the equation $g = f - 17$ . If we add $g$ to both sides of the equation $f - g = 17$ , we get $f = g + 17$ , which is equivalent to $g = f - 17$ when solved for $g$ .
Evaluate Option (B): (C) $fg = 17$ suggests that the product of the number of tickets sold by Finn and Gabby is $17$ , which is not related to the information given in the problem.
Evaluate Option (C): (D) $\frac{f}{g} = 17$ suggests that the ratio of the number of tickets sold by Finn to the number of tickets sold by Gabby is $17$ , which is also not related to the information given in the problem.
Evaluate Option (D): Based on the steps above, the correct representation of the relationship between the number of tickets Finn sold and the number of tickets Gabby sold is given by option (B) $f - g = 17$ .