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 September 19th, 2018, 12:18 AM #1 Member   Joined: Sep 2018 From: Japan Posts: 35 Thanks: 2 Number of muffins in a bakery In a bakery, (1/4) of the muffins for sale are banana muffins, (2/5) are walnut muffins and the rest are chocolate muffins. There are 18 more chocolate muffins than banana muffins. How many muffins are there for sale altogether? My work: Number of chocolate = C Number of walnut = W Number of banana = B [1] banana muffins are (1/4) of the total muffins [2]Walnut muffins are (2/5) of the total muffins [3]There are 18 more cocolate muffins than banana muffins. so, C = B + 18 from [1], 1 - (1/4) = 3/4 muffins remaining. from [2], I'm not sure why they did (3/4) - (2/5) = (7/20). Unless the wording is suppose to be this way. "In a bakery, (1/4) of the muffins for sale are banana muffins, and the remaining (2/5) are walnut muffins and the rest are chocolate muffins." Then I got stuck from [2] by not getting to one of the correct paths.
 September 19th, 2018, 04:01 AM #2 Global Moderator   Joined: Dec 2006 Posts: 19,988 Thanks: 1855 The stated problem implies B = 45, W = 72, and C = 63, so there are 180 muffins for sale in total. If that isn't the intended solution, the wording of the problem needs amendment. Thanks from JeffM1 and xoritos
September 19th, 2018, 10:52 AM   #3
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Quote:
 Originally Posted by xoritos In a bakery, (1/4) of the muffins for sale are banana muffins, (2/5) are walnut muffins and the rest are chocolate muffins. There are 18 more chocolate muffins than banana muffins. How many muffins are there for sale altogether? Number of chocolate = c Number of walnut = w Number of banana = b
Total muffins = t

b = t/4
w = 2t/5
c = b+18
c = t/4 + 18 [1]
also:
c = t - b - w
c = t - t/4 - 2t/5 [2]

[1] = [2]
t/4 + 18 = t - t/4 - 2t/5

Solve for t

September 19th, 2018, 01:58 PM   #4
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Quote:
 Originally Posted by xoritos In a bakery, (1/4) of the muffins for sale are banana muffins, (2/5) are walnut muffins and the rest are chocolate muffins. There are 18 more chocolate muffins than banana muffins. How many muffins are there for sale altogether? My work: Number of chocolate = C Number of walnut = W Number of banana = B [1] banana muffins are (1/4) of the total muffins [2]Walnut muffins are (2/5) of the total muffins [3]There are 18 more cocolate muffins than banana muffins. so, C = B + 18 from [1], 1 - (1/4) = 3/4 muffins remaining. from [2], I'm not sure why they did (3/4) - (2/5) = (7/20). Unless the wording is suppose to be this way. "In a bakery, (1/4) of the muffins for sale are banana muffins, and the remaining (2/5) are walnut muffins and the rest are chocolate muffins." Then I got stuck from [2] by not getting to one of the correct paths.
As denis indicated, your fundamental problem was not recognizing that there were FOUR unknowns. You were asked "how many muffins were for sale." Obviously that is not known so you were missing an unknown.

With four unknowns you need four independent and consistent equations.

$t = b + c + w.$

Notice that you were unable to translate the facts that you labelled 1 and 2 into equations. That was a clue that you had not associated each unknown with a unique symbol.

$b = \dfrac{1}{4} * t.$

$w = \dfrac{2}{5} * t.$

$c = b + 18.$

Now the step that you did not understand becomes

$b + c + w = t \implies c + w = t - b = t - \dfrac{1}{4} * t = \dfrac{3}{4} * t \implies$

$c = \dfrac{3}{4} * t - w = \dfrac{3}{4} * t - \dfrac{2}{5} * t = \dfrac{15 - 8}{20} * t = \dfrac{7}{20} * t.$

I am guessing that they then did

$c = b + 18 \implies \dfrac{7}{20} * t = \dfrac{1}{4} * t + 18 \implies \dfrac{7}{20} * t - \dfrac{1}{4} * t = 18 \implies$

$\dfrac{2}{20} * t = 18 \implies t = 180.$

EDIT: I must admit I find that a very ugly way to solve this system. I would do it as follows.

$b + c + w = t \implies 20b + 20c + 20w = 20t.$

$b = \dfrac{1}{4} * t \implies 20b = 5t.$

$c = b + 18 \implies 20c = 20b + 360 = 5t + 360.$

$w = \dfrac{2}{5} * t \implies 20w = 8t.$

$\therefore 20t = 5t + 5t + 360 + 8t = 18t + 360 \implies 2t = 360 \implies t = 180.$

BUT UNTIL YOU TRANSLATE THE PROBLEM INTO EQUATIONS, you do not have the luxury of figuring out a clean way to solve it. And you cannot translate into equations UNTIL YOU HAVE ASSIGNED A UNIQUE SYMBOL TO EACH UNKNOWN.

Last edited by JeffM1; September 19th, 2018 at 02:13 PM.

September 19th, 2018, 11:47 PM   #5
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Quote:
 Originally Posted by Denis Total muffins = t b = t/4 w = 2t/5 c = b+18 c = t/4 + 18
Follwing what Denis wrote.

This is what I did.

Number of chocolate = C
Number of walnut = W
Number of banana = B
Number of Total = T

B + W + C = T

(T/4) + (2T/5) + T/4 + 18 = T

T = 180.

If that's wrong, please let me know.

Thank you to everyone who helped

 September 20th, 2018, 12:14 AM #6 Global Moderator   Joined: Dec 2006 Posts: 19,988 Thanks: 1855 It's correct. Thanks from xoritos

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