Calculate the total number of ratio parts.

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to solve the problem about sharing rice:

Calculate the total number of ratio parts.
The ratio for Mary, Joan, and Agnes is $2:4:3$ .
$\text{Total parts} = 2 + 4 + 3 = 9$
Determine the value of one ratio part in kilograms.
The total amount of rice is $810\, \text{kg}$ .
$\text{Value per part} = \frac{810\, \text{kg}}{9} = 90\, \text{kg/part}$
Calculate each person's share in kilograms.
Mary's share: $2 \times 90\, \text{kg} = 180\, \text{kg}$
Joan's share: $4 \times 90\, \text{kg} = 360\, \text{kg}$
Agnes's share: $3 \times 90\, \text{kg} = 270\, \text{kg}$
Convert each person's share from kilograms (kg) to hectograms (Hg).
Recall that $1\, \text{kg} = 10\, \text{Hg}$ .
Mary's share: $180\, \text{kg} \times 10\, \text{Hg/kg} = 1800\, \text{Hg}$
Joan's share: $360\, \text{kg} \times 10\, \text{Hg/kg} = 3600\, \text{Hg}$
Agnes's share: $270\, \text{kg} \times 10\, \text{Hg/kg} = 2700\, \text{Hg}$

Mary got $\boxed{\text{1800 Hg}}$ .
Joan got $\boxed{\text{3600 Hg}}$ .
Agnes got $\boxed{\text{2700 Hg}}$ .

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