Tiara has 12 large cans of fire-engine red paint. The smaller paint cans resting on
the table can each hold ⅗ as much paint as a large can. How many small cans
will Tiara be able to fill?
To find out how many small cans Tiara will be able to fill, we need to compare the capacity of the small cans to that of the large cans.
Given that the smaller cans can each hold ⅗ as much paint as a large can, it means they have a capacity of 3/5 times the capacity of a large can.
To get the capacity of a small can relative to a large can, we can multiply the capacity of a large can by 3/5. Let's calculate it:
Capacity of a small can = (3/5) * Capacity of a large can
Since the problem does not provide the capacity of a large can, we will assume it as a variable, let's call it 'L'. Therefore:
Capacity of a small can = (3/5) * L
Now, let's substitute the given information that Tiara has 12 large cans of fire-engine red paint:
Capacity of small cans = (3/5) * Capacity of a large can
Capacity of small cans = (3/5) * L
Tiara has 12 large cans, so the number of small cans she can fill will be the total capacity of the large cans divided by the capacity of a small can:
Number of small cans = Total capacity of large cans / Capacity of a small can
Number of small cans = (12 * Capacity of a large can) / (3/5) * Capacity of a large can
The Capacity of a large can cancels out:
Number of small cans = 12 / (3/5)
Number of small cans = 12 * (5/3)
Number of small cans = 20
Therefore, Tiara will be able to fill 20 small cans.