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A jar contains some cookies. The weight of the jar and cookies is 700g. Meghan eats $\frac{4}{5}$ of the cookies. The weight of the jar and cookies is now 400g. How much does the jar weigh? How many cookies were there from the start?

What I did: $\frac{700}{5}$ = 140

700 - 140 = 560

560 - 400 = 160

But I don't know what to do next.

Thank You and Help is appreciated

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    $\begingroup$ Looks a bit random and you have poor Meghan eating some of the jar. If X is the weight of the jar and Y the weight of the cookies can you write down two equations relating X and Y? $\endgroup$ – Paul Sep 29 '18 at 7:48
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    $\begingroup$ $x$ + $y$ = 700 $\endgroup$ – xx_Gcsemathstudent_xx Sep 29 '18 at 7:52
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    $\begingroup$ Ohh wait is it 1/5 $\endgroup$ – xx_Gcsemathstudent_xx Sep 29 '18 at 7:58
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    $\begingroup$ Using simultaneous equations I found out that x = 325 so the jar weighs 325g $\endgroup$ – xx_Gcsemathstudent_xx Sep 29 '18 at 8:27
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    $\begingroup$ Just a poorly worded question. There are 375g of cookies. $\endgroup$ – Paul Sep 29 '18 at 12:08
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You should assign letters to the unknown quantities and form simultaneous equations from them.

I would let the jar's weight be $J$ and the total weight of the cookies be $C$.

The first statement tells you:

$$J+C=700\tag 1$$

Then Meghan eats $\frac 45$ of the cookies, and the new total weight is $400g$. Can you then see that this means:

$$J +\frac15 C = 400 \tag 2$$

You now have a pair of simultaneous equations. Im sure you know how to continue this.

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The problem does not seem well put with respect to the number of cookies, as long as the weight of one cookie is not given. Let

  • $j$ - weight of jar
  • $n$ - number of cookies at the beginning
  • $c$ - weight of one cookie

Then you have \begin{eqnarray} j + n\cdot c & = & 700 \\ j + \frac{n}{5}\cdot c & = & 400 \end{eqnarray} $$\Rightarrow \frac{4}{5}\cdot n\cdot c = 300$$ $$\Rightarrow n\cdot c = \frac{5}{4}\cdot 300 = 375 = 3\cdot 5^3$$

Restricting our consideration to integers you may have at the beginning, for example:

  • $125$ cookies $3g$ each
  • $25$ cookies $15g$ each
  • $15$ cookies $25g$ each
  • etc.
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