Respuesta :
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;
[tex]x+y =250 \ \ \ \ equation \ 1[/tex]
Also Given:
Maria used 18 beads to make a bracket.
hence bead left with maria = [tex]x-18[/tex]
farida gave away 2/5 of her beads.
Hence beads left with Farida = [tex]y - \frac{2}{5}y= \frac{5y}{5}-\frac{2y}{5}=\frac{5y-2y}{5}=\frac{3y}{5}[/tex]
Also they have the same number of beads left.
bead left with maria = beads left with Farida
[tex]x-18= \frac{3y}{5}\\5(x-18)=3y\\5x-90=3y\\5x-3y =90 \ \ \ \ equation \ 2[/tex]
Now Multiplying equation 1 with 3 we get;
[tex]3(x+y)=3\times250 = 3x+3y = 750 \ \ \ \ equation \ 3[/tex]
Now adding equation 2 by equation 3 we get;
[tex](5x-3y)+(3x+3y) = 750+90\\5x-3y+3x+3y = 840\\8x=840\\x=\frac{840}{8}=105[/tex]
we know the value of x = 105
hence substituting value of x in equation 1 we get;
[tex]105+y=250\\y=250-105 =145[/tex]
Maria had 105 beads and Farida had 145 beads at first.
Final Answer: Maria had 105 beads at first.
