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Sagot :
Using a system of equations, it is found that the earnings of Mohammed are given by: 18,212 aed.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
- Variable x: Earnings of Ahmed.
- Variable y: Earnings of Bekhit.
- Variable z: Earnings of Saeed.
- Variable w: Earnings of Mohammed.
The earnings of ahmed and bekhit are in the ratio 3:7, hence:
[tex]\frac{x}{y} = \frac{3}{7}[/tex]
[tex]3y = 7x[/tex]
[tex]y = \frac{7x}{3}[/tex]
That of bekhit and saeed is 4:9, hence:
[tex]\frac{y}{z} = \frac{4}{9}[/tex]
[tex]4z = 9y[/tex]
[tex]z = \frac{9y}{4}[/tex]
[tex]z = \frac{63x}{12}[/tex]
The ratio of mohammed and saeed is 7:6, hence:
[tex]\frac{z}{w} = \frac{7}{6}[/tex]
[tex]7w = 6z[/tex]
[tex]w = \frac{6z}{7}[/tex]
[tex]w = \frac{378x}{84}[/tex]
The sum is of 52950, hence:
[tex]x + y + z + w = 52950[/tex]
[tex]x + \frac{7x}{3} + \frac{63x}{12} + \frac{378x}{84} = 52950[/tex]
[tex]1099x = 52950 \times 84[/tex]
[tex]x = \frac{52950 \times 84}{1099}[/tex]
[tex]x = 4047[/tex]
Hence, Mohammed earnings in aed are given as follows:
[tex]w = \frac{378 \times 4047}{84} = 18212[/tex]
More can be learned about a system of equations at https://brainly.com/question/24342899
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