Final answer:
Melanie can paint a total of 10 bookcases with 1 7/8 gallons of paint by converting the gallons into sixteenths and dividing by the amount needed per bookcase.
Step-by-step explanation:
To determine how many bookcases Melanie can paint with 1 7/8 gallons of paint when each bookcase requires 3/16 gallon of paint, we first convert the total paint quantity into sixteenths to align with the measurement used per bookcase.
Since there are 16 sixteenths in a whole gallon, 1 gallon is equal to 16/16. Thus, 7/8 of a gallon is equal to 14 sixteenths (7/8 multiplied by 16/16). The whole measurement in sixteenths is (16/16 × 1) + 14/16 which equals to 30/16 or 1 14/16 gallons. To further simplify, 30/16 = 16/16 + 14/16 which is 1 gallon + 14/16, so we have:
- 1 gallon = 16/16
- 7/8 of a gallon = 14/16
- Total paint = 1 gallon + 7/8 gallon = 16/16 + 14/16 = 30/16 gallons
Once we have converted 1 7/8 gallons to sixteenths, we have 30/16 gallons, which can be expressed in sixteenths as 30 sixteenths.
To find the total number of bookcases Melanie can paint, we divide the total paint available in sixteenths by the amount needed per bookcase, also in sixteenths. Thus, we have:
(30/16) / (3/16) = 30 / 3 = 10 bookcases.
Therefore, Melanie can paint a total of 10 bookcases with 1 7/8 gallons of paint.