Respuesta :
Solving the system of equations obtained by the substitution method, we can conclude that Adam had 225 beads at first.
How to solve a system of equations by substitution method?
- A system of equations is a finite set of equations containing two or more variables for which we seek a general solution.
- For example, consider a system of two equations in two variables [tex]x[/tex], [tex]y[/tex]:[tex]a_1x+b_1y=c_1\\a_2x+b_2y=c_2[/tex]
- To solve this system, we can use the substitution method which is one of the widely used methods for solving a system of linear equations. In this method, we solve the first equation for [tex]x[/tex] (or [tex]y[/tex]) in terms of [tex]y[/tex] (or [tex]x[/tex]) and then substitute that expression for [tex]x[/tex] (or [tex]y[/tex]) in the second equation. Then we obtain an equation that contains only one variable [tex]y[/tex] (or [tex]x[/tex]) and can easily solve it.
Let us suppose Adam had [tex]x[/tex] beads and Rahmad had [tex]y[/tex] beads.
By the problem, if Adam gave [tex]\frac{1}{3}[/tex] of his share to Rahmad, then Rahmad would have [tex]70[/tex] more than Adam. This can be expressed by the following equation:
[tex]y+\frac{x}{3}-(x-\frac{x}{3})=70\\\Longrightarrow y-\frac{x}{3}=70[/tex] (1)
Again, if Adam gave [tex]\frac{1}{5}[/tex] of his share to Rahmad, then Rahmad would have [tex]10[/tex] more than Adam. This can be expressed by the following equation:
[tex]y+\frac{x}{5}-(x-\frac{x}{5})=10\\\Longrightarrow y-\frac{3x}{5}=10[/tex] (2)
From equation (1), we get: [tex]y=\frac{x}{3}+70[/tex].
Now, substituting this value of [tex]y=\frac{x}{3}+70[/tex] in the equation (2), we obtain:
[tex]\frac{x}{3}+70-\frac{3x}{5}=10\\\Longrightarrow \frac{4x}{15}=60\\\Longrightarrow x=\frac{60\times 15}{4}\\\therefore x=225[/tex]
Then [tex]y=\frac{225}{3}+70=145[/tex].
Thus, at first, Adam had 225 beads.
Therefore, by solving the system of equations by substitution method, we can conclude that Adam had 225 beads at first.
To know more about the substitution method, refer: https://brainly.com/question/22340165
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