Ratio and Proportion Maths Problem Solving

Question

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

Answer 1

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.

Answer 2

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.