Container A has twice the capacity of container B. Container A is full of sand and container B is empty. Suppose 1/8 of the sand in container B will contain A is poured into container B. What fractional part of container B will contain sand?
To find out what fractional part of container B will contain sand, we first need to determine the amount of sand that is being poured into container B.
Given that 1/8 of the sand in container A is poured into container B, we can express this mathematically as:
Amount of sand poured into B = (1/8) * amount of sand in A
Since container A has twice the capacity of B, we can say that the amount of sand in A is twice the amount of sand in B.
Amount of sand in A = 2 * amount of sand in B
Substituting this into the previous equation, we have:
Amount of sand poured into B = (1/8) * (2 * amount of sand in B)
Simplifying, we get:
Amount of sand poured into B = (1/8) * (2B) = B/4
So, container B will have B/4 sand.
To express this as a fractional part of container B, we can rewrite it as:
Fraction of container B containing sand = Amount of sand in B / Capacity of container B
Fraction of container B containing sand = (B/4) / B
Simplifying further, we see that the B's cancel out:
Fraction of container B containing sand = 1/4
Therefore, 1/4 or one-fourth of container B will contain sand.