- Thread starter Meechee
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Have you used algebra before?

Please show any work that you've tried. Cheers

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If you're supposed to use arithmetic, then you can guess-and-check.

If 1/5th of something is used, then 4/5ths remains. If 1/7th of something is used, then 6/7ths remains.

We know that any egg-counts in this exercise are Whole numbers. This tells us the beginning number of eggs must be a multiple of both 5 and 7 (otherwise, dividing by 5 or by 7 would result in a partial egg).

We also know that after using 1/7th of the remaining eggs on Tuesday, the number of eggs left must be 132 less than the beginning number on Monday. In other words, the first multiple of 5 and 7 (which is 35) is too small.

So, try checking larger multiples (i.e., multiply 35 by Whole numbers 4,5,6,…, and check each result). You won't need to check more than 10 possibilities, before finding the answer.

EG:

\(\displaystyle 4\times35 = 140 \text{ eggs}\\

\;\\

\dfrac{4}{5} \times \dfrac{140}{1} = 112\\

\;\\

\dfrac{6}{7} \times \dfrac{112}{1} = 96\\

\;\\

96 + 132 \ne 140\)

140 is too small, so check 5×35 next.

Cheers

There's a way to combine the two steps of taking 4/5ths followed by taking 6/7ths of the result into a single step.

PS: Using algebra is easier, if you're allowed to do that.

EDIT: Replaced symbol ∙ with × in example.

If 1/5th of something is used, then 4/5ths remains. If 1/7th of something is used, then 6/7ths remains.

We know that any egg-counts in this exercise are Whole numbers. This tells us the beginning number of eggs must be a multiple of both 5 and 7 (otherwise, dividing by 5 or by 7 would result in a partial egg).

We also know that after using 1/7th of the remaining eggs on Tuesday, the number of eggs left must be 132 less than the beginning number on Monday. In other words, the first multiple of 5 and 7 (which is 35) is too small.

So, try checking larger multiples (i.e., multiply 35 by Whole numbers 4,5,6,…, and check each result). You won't need to check more than 10 possibilities, before finding the answer.

\(\displaystyle 4\times35 = 140 \text{ eggs}\\

\;\\

\dfrac{4}{5} \times \dfrac{140}{1} = 112\\

\;\\

\dfrac{6}{7} \times \dfrac{112}{1} = 96\\

\;\\

96 + 132 \ne 140\)

140 is too small, so check 5×35 next.

Cheers

There's a way to combine the two steps of taking 4/5ths followed by taking 6/7ths of the result into a single step.

PS: Using algebra is easier, if you're allowed to do that.

EDIT: Replaced symbol ∙ with × in example.

Last edited:

I still don’t get it!If you're supposed to use arithmetic, then you can guess-and-check.

If 1/5th of something is used, then 4/5ths remains. If 1/7th of something is used, then 6/7ths remains.

We know that any egg-counts in this exercise are Whole numbers. This tells us the beginning number of eggs must be a multiple of both 5 and 7 (otherwise, dividing by 5 or by 7 would result in a partial egg).

We also know that after using 1/7th of the remaining eggs on Tuesday, the number of eggs left must be 132 less than the beginning number on Monday. In other words, the first multiple of 5 and 7 (which is 35) is too small.

So, try checking larger multiples (i.e., multiply 35 by Whole numbers 4,5,6,…, and check each result). You won't need to check more than 10 possibilities, before finding the answer.

EG:

\(\displaystyle 4\cdot35 = 140 \text{ eggs}\\

\;\\

\dfrac{4}{5} \cdot \dfrac{140}{1} = 112\\

\;\\

\dfrac{6}{7} \cdot \dfrac{112}{1} = 96\\

\;\\

96 + 132 \ne 140\)

140 is too small, so check 5∙35 next.

Cheers

There's a way to combine taking 4/5ths followed by taking 6/7ths of the result into a single step.

PS: Using algebra is easier, if you're allowed to do that.

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Did you read the guidelines, at the link provided in post #2?I still don’t get it!

Show what you tried, or explain

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Can you please tell us which part you did not understand in the previous post? Can you use algebra? We will help you but we need to know where you need help.I still don’t get it!

I added 1/5 and 1/7 and got 12/35 I subtracted 132-35 and got 97.Can you please tell us which part you did not understand in the previous post? Can you use algebra? We will help you but we need to know where you need help.

Now I’m getting 420 35x5=175 35x7=245 175 + 235= 420Can you please tell us which part you did not understand in the previous post? Can you use algebra? We will help you but we need to know where you need help.

288 eggs?Did you read the guidelines, at the link provided in post #2?

Show what you tried, or explainwhyyou're stuck.

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Let x be the number of eggs.

On Monday you used 1/5 of the eggs leaving 4/5 of the eggs left, ie (4/5)x are left.

On Tuesday you used 1/7 of the remaining eggs, so you have 6/7 of the remaining eggs, ie (6/7) of (4/5)x, ie (6/7)*(4/5)x = (24/35)x

On Wednesday he bought another 132 eggs. That will be (24/35)x + 132 and this equals the original number of eggs, ie (24/35)x + 132 = x.

Can you solve this for x?

475

Let x be the number of eggs.

On Monday you used 1/5 of the eggs leaving 4/5 of the eggs left, ie (4/5)x are left.

On Tuesday you used 1/7 of the remaining eggs, so you have 6/7 of the remaining eggs, ie (6/7) of (4/5)x, ie (6/7)*(4/5)x = (24/35)x

On Wednesday he bought another 132 eggs. That will be (24/35)x + 132 and this equals the original number of eggs, ie (24/35)x + 132 = x.

Can you solve this for x?

175+ 168= 343 343+ 132= 475

Do you bother to read the answers that are posted? You were asked if you know algebra. There is an easy way to answer the question if you do.

If you do not know algebra, then there is a hard way to do it using just arithmetic.

You did not tell us how you came up with 475 so there is no way for us to tell you where you went wrong. Furthermore, you did not check your own work, whatever it was.

One fifth of 475 is 95. And 475 - 95 = 380. But 380 = 2 * 2 * 5 * 19 is

The algebra way:

\(\displaystyle x = \text {original number of eggs.}\)

\(\displaystyle \left \{ \left ( (1 - \dfrac{1}{7} \right ) * \left ( 1 - \dfrac{1}{5} \right ) * x \right \} + 132 = x \implies \left ( \dfrac{6}{7} * \dfrac{4}{5} * x \right ) + 132 = x\implies\)

\(\displaystyle \dfrac{24x}{35} + 132 = \dfrac{35x}{35} \implies 132 = \dfrac{35x - 24x}{35} = \dfrac{11x}{35} \implies\)

\(\displaystyle x = \dfrac{35 * 132}{11} = 35 * 12 = 420.\)

Let's check.

One fifth of 420 is 84. And 420 - 84 = 336. One seventh of 336 is 48. And 336 - 48 = 288. And 288 + 132 = 420.

What is it that you do not understand about the algebra shown above?

I do not understand algebra

Do you bother to read the answers that are posted? You were asked if you know algebra. There is an easy way to answer the question if you do.

If you do not know algebra, then there is a hard way to do it using just arithmetic.

You did not tell us how you came up with 475 so there is no way for us to tell you where you went wrong. Furthermore, you did not check your own work, whatever it was.

One fifth of 475 is 95. And 475 - 95 = 380. But 380 = 2 * 2 * 5 * 19 isNOTevenly divisible by 7. So that answer is wrong.

The algebra way:

\(\displaystyle x = \text {original number of eggs.}\)

\(\displaystyle \left \{ \left ( (1 - \dfrac{1}{7} \right ) * \left ( 1 - \dfrac{1}{5} \right ) * x \right \} + 132 = x \implies \left ( \dfrac{6}{7} * \dfrac{4}{5} * x \right ) + 132 = x\implies\)

\(\displaystyle \dfrac{24x}{35} + 132 = \dfrac{35x}{35} \implies 132 = \dfrac{35x - 24x}{35} = \dfrac{11x}{35} \implies\)

\(\displaystyle x = \dfrac{35 * 132}{11} = 35 * 12 = 420.\)

Let's check.

One fifth of 420 is 84. And 420 - 84 = 336. One seventh of 336 is 48. And 336 - 48 = 288. And 288 + 132 = 420.

What is it that you do not understand about the algebra shown above?

The second post in this thread asked you whether you knew algebra. You have wasted a ton of time by not answering that question.I do not understand algebra

So. What fraction of the original number of eggs is left after Monday?

Of the number of eggs left at the end of the end of Monday, what fraction will be left after Tuesday?

But that means what fraction of the

So what fraction of the original number of eggs does it take to get us back to where we started?

Based on your post # 17, I think you are VERY close to getting the correct answer by using arithmetic. So please answer the questions above.

Why? Teacher absent?I do not understand algebra

What grade are you in?