To repartir $1513 inversely proportional to 4, 6, and 9, we calculate the sum of the inverses of those numbers, determine each proportion, and then allocate the funds accordingly, resulting in $717.27, $478.18, and $317.55 being distributed to each part.
To repartir $1513 en partes inversamente proporcionales a 4, 6, and 9, we need to first find the inverse of each number and then determine the individual parts of the total sum based on these inverses.
The inverses of 4, 6, and 9 are ¹⁄₄, ¹⁄₆, and ¹⁄₉ respectively. To calculate the proportional parts, we sum the inverses:
Sum of inverses = ¹⁄₄ + ¹⁄₆ + ¹⁄₉
Sum of inverses = 0.25 + 0.1667 + 0.1111 = 0.5278
Now, we find the proportion for each inverse:
Proportion for 4: $1513 * (¹⁄₄ / 0.5278)
Proportion for 6: $1513 * (¹⁄₆ / 0.5278)
Proportion for 9: $1513 * (¹⁄₉ / 0.5278)
Finally, we calculate the actual amounts:
Amount for 4: $1513 * (0.25 / 0.5278) = $717.27 (approximately)
Amount for 6: $1513 * (0.1667 / 0.5278) = $478.18 (approximately)
Amount for 9: $1513 * (0.1111 / 0.5278) = $317.55 (approximately)
So, the amounts to be distributed inversely proportional to 4, 6, and 9 are $717.27, $478.18, and $317.55 respectively (rounding to two decimal places).