Bob used 1/5 of eggs Monday, 1/7 of remainder on Tues; bought 132 more Wed, equalling initial amt on Monday

Meechee

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Bob the baker had some eggs. He used 1/5 of them on Monday and 1/7 of the rest on Tuesday. he bought another 132 eggs on Wednesday and then he had as many eggs as he had at first. How many eggs did he have at first?
 

mmm4444bot

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Hello Meechee. Your duplicate thread has been deleted. Please read the forum's submission guidelines; you may start with this summary. Thank you!

Have you used algebra before?

Please show any work that you've tried. Cheers

😎
 

Otis

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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.
 
Last edited:

Meechee

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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:

\(\displaystyle 4\cdot35 = 140 \text{ eggs}\\
\;\\
\dfrac{4}{5} \cdot \dfrac{140}{1} = 112\\
\;\\
\dfrac{6}{7} \cdot \dfrac{112}{1} = 96\\
\;\\
96 + 132 \ne 140\)


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.

😎
I still don’t get it! 😞
 

mmm4444bot

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

Show what you tried, or explain why you're stuck.

😎
 

Jomo

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I still don’t get it! 😞
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.
 

Meechee

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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 added 1/5 and 1/7 and got 12/35 I subtracted 132-35 and got 97.
 

Meechee

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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.
Now I’m getting 420 35x5=175 35x7=245 175 + 235= 420
 

Meechee

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420-132= 288 eggs??
 

Meechee

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Denis

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Can you "see" that 288 is impossible: can't be divided by 5 unless you break an egg :)
Hint:

f = eggs at first

f - f/5 - (f - f/5)/7 + 132 = f
 

Jomo

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Let's see if you are correct. On Monday you used 1/5 of the eggs. Now 1/5 of 288 is 57.6. So the number of eggs used on Monday was 57.6. Does this make sense.

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?
 

Meechee

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Let's see if you are correct. On Monday you used 1/5 of the eggs. Now 1/5 of 288 is 57.6. So the number of eggs used on Monday was 57.6. Does this make sense.

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
 

Denis

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I gave you this earlier:
f = eggs at first
f - f/5 - (f - f/5)/7 + 132 = f

Can you not solve that?
 

JeffM

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Meechee

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 NOT evenly 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?
 

Meechee

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11•35= 385
 

Meechee

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Meechee

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 NOT evenly 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?
I do not understand algebra
 

JeffM

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

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 original number of eggs will be left after Tuesday?.

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.
 

Denis

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