Question

Maria and farida has 250 beads altogether. After Maria used 18 beads to make a bracket and farida gave away 2/5 of her beads, they have the same number of beads left. How many beads did Maria have at first?

Answer 1

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;

$x+y =250 \ \ \ \ equation \ 1$

Also Given:

Maria used 18 beads to make a bracket.

hence bead left with maria = $x-18$

farida gave away 2/5 of her beads.

Hence beads left with Farida = $y - \frac{2}{5}y= \frac{5y}{5}-\frac{2y}{5}=\frac{5y-2y}{5}=\frac{3y}{5}$

Also they have the same number of beads left.

bead left with maria = beads left with Farida

$x-18= \frac{3y}{5}\\5(x-18)=3y\\5x-90=3y\\5x-3y =90 \ \ \ \ equation \ 2$

Now Multiplying equation 1 with 3 we get;

$3(x+y)=3\times250 = 3x+3y = 750 \ \ \ \ equation \ 3$

Now adding equation 2 by equation 3 we get;

$(5x-3y)+(3x+3y) = 750+90\\5x-3y+3x+3y = 840\\8x=840\\x=\frac{840}{8}=105$

we know the value of x = 105

hence substituting value of x in equation 1 we get;

$105+y=250\\y=250-105 =145$

Maria had 105 beads and Farida had 145 beads at first.

Final Answer: Maria had 105 beads at first.