Answer:
2 mangoes
Step-by-step explanation:
oan's share: Since the ratio is 4:1, Joan received 4/5 (four-fifths) of the total mangoes (x). This translates to (4/5) * x mangoes for Joan.
Joan's remaining mangoes: We are given that after sharing some mangoes with June, Joan remained with 5 mangoes. This tells us that (4/5) * x - (3/8) * [(4/5) * x] = 5.
Simplifying the equation:
Combine like terms: [(32/40) * x - (15/40) * x] = 5
This simplifies to (17/40) * x = 5
Solving for x (total mangoes):
Multiply both sides by 40/17 to isolate x: x = (5 * 40) / 17 ≈ 11.76 (rounded to two decimal places)
Since the total number of mangoes cannot be a fraction, we can round 11.76 up to 12. This is a reasonable assumption as the question asks for the whole number of mangoes Kyle received.
Kyle's share:
We know the ratio is 4:1 (Joan:Kyle).
Since the total is approximately 12 mangoes, Kyle received (1/5) * 12 = 2.4 mangoes.
Again, the number of mangoes cannot be a fraction. Kyle cannot receive a fraction of a mango.
Here's the key point:
The total number of mangoes shared (x) cannot be definitively determined because it results in a fractional value after rounding.
Possible Solutions:
There are two possible scenarios depending on whether we round the total number of mangoes up or down:
Scenario 1 (Rounding down total to 11):
In this case, Joan receives (4/5) * 11 = 8.8 mangoes.
Following the logic of sharing 3/8 with June, Joan would be left with 8.8 - (3/8) * 8.8 ≈ 5.5 mangoes.
This creates a discrepancy as we cannot have half a mango.
Scenario 2 (Rounding up total to 12):
This is the more likely scenario considering it aligns better with Joan's remaining mangoes (5).
Kyle receives (1/5) * 12 = 2.4 mangoes.
As discussed earlier, fractions of mangoes are not possible.
Therefore, considering the limitations of the problem and the context of Joan having 5 mangoes remaining, the most reasonable answer is:
Kyle received approximately 2 mangoes.
