# Ratio and Proportion Maths Problem Solving

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

• 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? – Paul Sep 29 '18 at 7:48
• $x$ + $y$ = 700 – xx_Gcsemathstudent_xx Sep 29 '18 at 7:52
• Ohh wait is it 1/5 – xx_Gcsemathstudent_xx Sep 29 '18 at 7:58
• Using simultaneous equations I found out that x = 325 so the jar weighs 325g – xx_Gcsemathstudent_xx Sep 29 '18 at 8:27
• Just a poorly worded question. There are 375g of cookies. – Paul Sep 29 '18 at 12:08

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.

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.