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

Maria had 105 beads at first.

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 - (2)/(5)y= (5y)/(5)-(2y)/(5)=(5y-2y)/(5)=(3y)/(5)`

Also they have the same number of beads left.

bead left with maria = beads left with Farida

`x-18= (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*250 = 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=(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.