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Mrs. Konings likes to eat Nerds (the candy, not her people). There are 1,000 Nerds in the box. The amount of Nerds left in the box decreases by a third each time she dumps out a portion. Let x represent the number of portions Mrs. Konings has taken and y represent the number of Nerds left in the box. Write an equation that represents the solution. (1 Point)

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Answer:

[tex]y-\frac{1}{3}+y=1000[/tex]

x=499.83

y=500.16

Step-by-step explanation:

We can solve this problem with a system of equations:

The total quantity of Nerds in the box:

[tex]x+y=1000[/tex] (1)

The amount of Nerds left in the box: [tex]y[/tex]

The number of portions Mrs. Konings has taken: [tex]x[/tex]

The amount of Nerds left in the box decreases by a third each time she dumps out a portion:

[tex]x=y-\frac{1}{3}[/tex] (2)

Substituting (2) in (1):

[tex]y-\frac{1}{3}+y=1000[/tex] (3) This is the equation

Let's find [tex]y[/tex]:

[tex]y=\frac{3001}{6}=500.16[/tex] (4)

Now let's find [tex]x[/tex] by substituting (4) in (2):

[tex]x=500.16-\frac{1}{3}=499.83[/tex] (5)

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