Maria had 105 beads at first.
Step-by-step explanation:
Let,
Beads Maria have = x
Beads Bear have = y
According to given statement;
x+y=250 Eqn 1
after Maria used 18 beads to make a bracelet and bear gave away 2/5 of her beads they have the same number of beads left.
x-18=[tex]y-\frac{2}{5}y[/tex]
Taking LCM on right side
[tex]x-18=\frac{5y-2y}{5}\\x-18=\frac{3y}{5}[/tex]
Multiplying both sides by 5
[tex]5(x-18)=5*\frac{3y}{5}\\5x-90=3y\\3y=5x-90\ \ \ Eqn\ 2[/tex]
From Eqn 1;
x=250-y
Putting this in Eqn 2;
[tex]3y=5(250-y)-90\\3y=1250-5y-90\\3y+5y=1160\\8y=1160\\[/tex]
Dividing both sides by 8
[tex]\frac{8y}{8}=\frac{1160}{8}\\y=145[/tex]
Putting y=145 in Eqn 1
[tex]x+145=250\\x=250-145\\x=105[/tex]
Maria had 105 beads at first.
Keywords: linear equation, substitution method
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