Answer:
a) The total weight of fruits is [tex]8\,\frac{1}{4}[/tex] kilograms, b) The weight of the fruits left is [tex]4\,\frac{1}{2}[/tex] kilograms.
Step-by-step explanation:
a) The total weight of fruits ([tex]m_{T}[/tex]) is calculated by the following formula:
[tex]m_{T} = m_{a} + m_{m}+m_{o}[/tex]
Where:
[tex]m_{a}[/tex] - Total weight of apples, measured in kilograms.
[tex]m_{m}[/tex] - Total weight of mangoes, measured in kilograms.
[tex]m_{o}[/tex] - Total weight of oranges, measured in kilograms.
If [tex]m_{a} = 1\,\frac{1}{2} \,kg[/tex], [tex]m_{m} = 5\,\frac{1}{4}\,kg[/tex] and [tex]m_{o} = 1\,\frac{1}{2}\,kg[/tex], then:
[tex]m_{T} = 1\,\frac{1}{2}\,kg + 5\,\frac{1}{4}\,kg + 1\,\frac{1}{2}\,kg[/tex]
[tex]m_{T} = \frac{6}{4}\,kg + \frac{21}{4}\,kg + \frac{6}{4}\,kg[/tex]
[tex]m_{T} = \frac{33}{4}\,kg[/tex]
[tex]m_{T} = 8\,\frac{1}{4}\,kg[/tex]
The total weight of fruits is [tex]8\,\frac{1}{4}[/tex] kilograms.
b) The weight eaten by her family is determined by the following expression:
[tex]m_{E} = m_{a,e} + m_{m,e} + m_{o,e}[/tex]
Where:
[tex]m_{a,e}[/tex] - Eaten weight of apples, measured in kilograms.
[tex]m_{m,e}[/tex] - Eaten weight of mangoes, measured in kilograms.
[tex]m_{o,e}[/tex] - Eaten weight of oranges, measured in kilograms.
Given that [tex]m_{a,e} = \frac{3}{4}\,kg[/tex], [tex]m_{m,e} = 2\,\frac{1}{2}\,kg[/tex] and [tex]m_{o,e} = \frac{1}{2}\,kg[/tex], the weight eaten by her family is:
[tex]m_{E} = \frac{3}{4}\,kg + 2\,\frac{1}{2}\,kg + \frac{1}{2}\,kg[/tex]
[tex]m_{E} = \frac{3}{4}\,kg + \frac{10}{4}\,kg + \frac{2}{4}\,kg[/tex]
[tex]m_{E} = \frac{15}{4}\,kg[/tex]
[tex]m_{E} = 3\,\frac{3}{4}\,kg[/tex]
The weight of the fruits left is found by subtraction:
[tex]m_{R} = m_{T}-m_{E}[/tex]
[tex]m_{R} = 8\,\frac{1}{4} \,kg -3\,\frac{3}{4}\,kg[/tex]
[tex]m_{R} = \frac{33}{4}\,kg-\frac{15}{4}\,kg[/tex]
[tex]m_{R} = \frac{18}{4}\,kg[/tex]
[tex]m_{R} = 4 \,\frac{1}{2}\,kg[/tex]
The weight of the fruits left is [tex]4\,\frac{1}{2}[/tex] kilograms.
