Answer:
a) The total weight of fruits is
kilograms, b) The weight of the fruits left is
kilograms.
Step-by-step explanation:
a) The total weight of fruits (
) is calculated by the following formula:
![m_{T} = m_{a} + m_{m}+m_{o}](https://tex.z-dn.net/?f=m_%7BT%7D%20%3D%20m_%7Ba%7D%20%2B%20m_%7Bm%7D%2Bm_%7Bo%7D)
Where:
- Total weight of apples, measured in kilograms.
- Total weight of mangoes, measured in kilograms.
- Total weight of oranges, measured in kilograms.
If
,
and
, then:
![m_{T} = 1\,\frac{1}{2}\,kg + 5\,\frac{1}{4}\,kg + 1\,\frac{1}{2}\,kg](https://tex.z-dn.net/?f=m_%7BT%7D%20%3D%201%5C%2C%5Cfrac%7B1%7D%7B2%7D%5C%2Ckg%20%2B%205%5C%2C%5Cfrac%7B1%7D%7B4%7D%5C%2Ckg%20%2B%201%5C%2C%5Cfrac%7B1%7D%7B2%7D%5C%2Ckg)
![m_{T} = \frac{6}{4}\,kg + \frac{21}{4}\,kg + \frac{6}{4}\,kg](https://tex.z-dn.net/?f=m_%7BT%7D%20%3D%20%5Cfrac%7B6%7D%7B4%7D%5C%2Ckg%20%2B%20%5Cfrac%7B21%7D%7B4%7D%5C%2Ckg%20%2B%20%5Cfrac%7B6%7D%7B4%7D%5C%2Ckg)
![m_{T} = \frac{33}{4}\,kg](https://tex.z-dn.net/?f=m_%7BT%7D%20%3D%20%5Cfrac%7B33%7D%7B4%7D%5C%2Ckg)
![m_{T} = 8\,\frac{1}{4}\,kg](https://tex.z-dn.net/?f=m_%7BT%7D%20%3D%208%5C%2C%5Cfrac%7B1%7D%7B4%7D%5C%2Ckg)
The total weight of fruits is
kilograms.
b) The weight eaten by her family is determined by the following expression:
![m_{E} = m_{a,e} + m_{m,e} + m_{o,e}](https://tex.z-dn.net/?f=m_%7BE%7D%20%3D%20m_%7Ba%2Ce%7D%20%2B%20m_%7Bm%2Ce%7D%20%2B%20m_%7Bo%2Ce%7D)
Where:
- Eaten weight of apples, measured in kilograms.
- Eaten weight of mangoes, measured in kilograms.
- Eaten weight of oranges, measured in kilograms.
Given that
,
and
, the weight eaten by her family is:
![m_{E} = \frac{3}{4}\,kg + 2\,\frac{1}{2}\,kg + \frac{1}{2}\,kg](https://tex.z-dn.net/?f=m_%7BE%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D%5C%2Ckg%20%2B%202%5C%2C%5Cfrac%7B1%7D%7B2%7D%5C%2Ckg%20%2B%20%5Cfrac%7B1%7D%7B2%7D%5C%2Ckg)
![m_{E} = \frac{3}{4}\,kg + \frac{10}{4}\,kg + \frac{2}{4}\,kg](https://tex.z-dn.net/?f=m_%7BE%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D%5C%2Ckg%20%2B%20%5Cfrac%7B10%7D%7B4%7D%5C%2Ckg%20%2B%20%5Cfrac%7B2%7D%7B4%7D%5C%2Ckg)
![m_{E} = \frac{15}{4}\,kg](https://tex.z-dn.net/?f=m_%7BE%7D%20%3D%20%5Cfrac%7B15%7D%7B4%7D%5C%2Ckg)
![m_{E} = 3\,\frac{3}{4}\,kg](https://tex.z-dn.net/?f=m_%7BE%7D%20%3D%203%5C%2C%5Cfrac%7B3%7D%7B4%7D%5C%2Ckg)
The weight of the fruits left is found by subtraction:
![m_{R} = m_{T}-m_{E}](https://tex.z-dn.net/?f=m_%7BR%7D%20%3D%20m_%7BT%7D-m_%7BE%7D)
![m_{R} = 8\,\frac{1}{4} \,kg -3\,\frac{3}{4}\,kg](https://tex.z-dn.net/?f=m_%7BR%7D%20%3D%208%5C%2C%5Cfrac%7B1%7D%7B4%7D%20%5C%2Ckg%20-3%5C%2C%5Cfrac%7B3%7D%7B4%7D%5C%2Ckg)
![m_{R} = \frac{33}{4}\,kg-\frac{15}{4}\,kg](https://tex.z-dn.net/?f=m_%7BR%7D%20%3D%20%5Cfrac%7B33%7D%7B4%7D%5C%2Ckg-%5Cfrac%7B15%7D%7B4%7D%5C%2Ckg)
![m_{R} = \frac{18}{4}\,kg](https://tex.z-dn.net/?f=m_%7BR%7D%20%3D%20%5Cfrac%7B18%7D%7B4%7D%5C%2Ckg)
![m_{R} = 4 \,\frac{1}{2}\,kg](https://tex.z-dn.net/?f=m_%7BR%7D%20%3D%204%20%5C%2C%5Cfrac%7B1%7D%7B2%7D%5C%2Ckg)
The weight of the fruits left is
kilograms.