Answer:Amy began with 9 marbles because tara had 6 for her 9
Step-by-step explanation:
Using proportions to build a system of equations, it is found that Amy began with 25 marbles.
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In our system, we are going to say that:
Amy began with 5 marbles for every 3 marbles that tara had.
This means that:
[tex]\frac{x}{y} = \frac{5}{3}[/tex]
We want x, thus:
[tex]3x = 5y[/tex]
[tex]y = \frac{3x}{5}[/tex]
After amy gave 1 marble to tara, amy ended up with 3 marbles for every 2 that tara had then.
This means that:
[tex]\frac{x - 1}{y + 1} = \frac{3}{2}[/tex]
[tex]2(x - 1) = 3(y + 1)[/tex]
[tex]2x - 2 = 3y + 3[/tex]
[tex]2x - 3y = 5[/tex]
Since [tex]y = \frac{3x}{5}[/tex]
[tex]2x - 3(\frac{3x}{5}) = 5[/tex]
Multiplying everything by 5:
[tex]10x - 9x = 25[/tex]
[tex]x = 25[/tex]
Amy began with 25 marbles.
A similar problem is given at https://brainly.com/question/24778333
