Answer:
Maria had 105 beads at first.
Step-by-step explanation:
Let number of beads Maria have be x.
Let number of beads Farida have be y.
Given:
Maria and Farida has 250 beads altogether.
Hence equation is represented as;
![x+y =250 \ \ \ \ equation \ 1](https://tex.z-dn.net/?f=x%2By%20%3D250%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%201)
Also Given:
Maria used 18 beads to make a bracket.
hence bead left with maria = ![x-18](https://tex.z-dn.net/?f=x-18)
farida gave away 2/5 of her beads.
Hence beads left with Farida = ![y - \frac{2}{5}y= \frac{5y}{5}-\frac{2y}{5}=\frac{5y-2y}{5}=\frac{3y}{5}](https://tex.z-dn.net/?f=y%20-%20%5Cfrac%7B2%7D%7B5%7Dy%3D%20%5Cfrac%7B5y%7D%7B5%7D-%5Cfrac%7B2y%7D%7B5%7D%3D%5Cfrac%7B5y-2y%7D%7B5%7D%3D%5Cfrac%7B3y%7D%7B5%7D)
Also they have the same number of beads left.
bead left with maria = beads left with Farida
![x-18= \frac{3y}{5}\\5(x-18)=3y\\5x-90=3y\\5x-3y =90 \ \ \ \ equation \ 2](https://tex.z-dn.net/?f=x-18%3D%20%5Cfrac%7B3y%7D%7B5%7D%5C%5C5%28x-18%29%3D3y%5C%5C5x-90%3D3y%5C%5C5x-3y%20%3D90%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%202)
Now Multiplying equation 1 with 3 we get;
![3(x+y)=3\times250 = 3x+3y = 750 \ \ \ \ equation \ 3](https://tex.z-dn.net/?f=3%28x%2By%29%3D3%5Ctimes250%20%3D%203x%2B3y%20%3D%20750%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%203)
Now adding equation 2 by equation 3 we get;
we know the value of x = 105
hence substituting value of x in equation 1 we get;
![105+y=250\\y=250-105 =145](https://tex.z-dn.net/?f=105%2By%3D250%5C%5Cy%3D250-105%20%3D145)
Maria had 105 beads and Farida had 145 beads at first.
Final Answer: Maria had 105 beads at first.