Answer:
6 bananas
Step-by-step explanation:
Here you want to know how many 3/8 lb bananas you need to arrive at BETWEEN 2 and 2 1/2 lbs of that fruit.
The appropriate inequality would be:
2 lb ≤ [ (3/8) lb ]x ≤ 2 1/2 lb.
We can make this problem easier to solve by using fractions throughout. The LCD here is 8. Note that 1 = 8/8 and 2 = 16/8. Also, 1/2 = 4/8, so that 2 1/2 = 2 4/8 = 20/8.
Then 2 lb ≤ [ (3/8) lb ]x ≤ 2 1/2 lb becomes:
16/8 lb ≤ (3/8 lb)x ≤ 20/8 lb. Multiplying this through by 8 to remove the fractions, we get:
16 ≤ 3x ≤ 20, '
Looking first at 16 ≤ 3x, we get 16/3 ≤ x or x ≥ 16/3. But we're speaking ONLY of WHOLE bananas, not thirds of bananas. Thus, x > 18/3, or x ≥ 6.
Going through a similar process with 3x ≤ 20, we get x ≤ 20/3. The first integer x value smaller than 20/3 is 18/3, or 6.
So there is only one possible value for x: It is 6, as in 6 bananas. This satisfies the original inequality 2 lb ≤ [ (3/8) lb ]x ≤ 2 1/2 lb.
