Lisa is decorating her office with two fully stocked aquariums. She saw an advertisement for Jorge's pet store in the newspaper. Jorge's store sells fish for aquariums. The table shows the fish Lisa buys from Jorge's pet store.
Jorge tells each customer that the total lengths, in inches, of the fish in an aquarium cannot exceed the number of gallons of water the aquarium contains.
The newspaper advertisement for Jorge's pet store has an illustration of a gold barb.
The illustration is not the same length as the actual gold barb. What was the scale factor used to create the illustration?
The scale factor used to create the illustration is 1.25.
The scale factor represents the ratio of the length of the illustration of the gold barb to its actual length. In this case, the illustration is larger than the actual fish, indicating a scale factor greater than 1.
A scale factor of 0.75 would imply that the illustration is 75% the size of the actual gold barb, making it smaller rather than larger. Since the problem specifies that the illustration is not the same length but does not indicate it is smaller, this choice is incorrect.
A scale factor of 1.25 indicates that the illustration is 125% the size of the actual gold barb. This means the illustration is larger than the fish, which aligns with the provided information about the illustration not matching the actual length. Thus, this is the correct answer.
A scale factor of 1.75 would suggest the illustration is 175% the size of the actual gold barb. While this indicates a larger illustration, it exceeds what is typically used for an aquarium fish in advertisements, making it less plausible than 1.25.
This option is the same as C and, for the same reasons, indicates a scale factor that is larger than necessary for an illustration of a gold barb. The preference for a more realistic representation suggests that 1.25 is a more suitable scale factor.
In conclusion, the scale factor of 1.25 correctly describes the relationship between the illustrated length of the gold barb and its actual size, indicating that the illustration is 25% larger than the real fish. The other options either suggest a smaller size or an impractically large representation, confirming that 1.25 is the most accurate scale factor for this scenario.
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