SOLUTION: Hi At a bakery the ratio of the number of lotus paste mooncakes to red bean paste mooncakes was 3 to 1 . The shop sold half of the total number of mooncakes. Out of the mooncakes

Question 1209419: Hi
At a bakery the ratio of the number of lotus paste mooncakes to red bean paste mooncakes was 3 to 1 . The shop sold half of the total number of mooncakes. Out of the mooncakes sold,5/6 were lotus paste. In the end there were 24 red bean left. How many lotus paste were sold. Upon question review there is a big gap under the question I do apologise

Found 5 solutions by ikleyn, greenestamps, math_tutor2020, mccravyedwin, AnlytcPhil:
Answer by ikleyn(52873)   (Show Source): You can put this solution on YOUR website!
.
Hi
At a bakery the ratio of the number of lotus paste mooncakes to red bean paste mooncakes was 3 to 1.
The shop sold half of the total number of mooncakes. Out of the mooncakes sold, 5/6 were lotus paste.
In the end there were 24 red bean left. How many lotus paste were sold.
Upon question review there is a big gap under the question I do apologise
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So, what do you want from us, the tutors?

Do you want we find and fix the gap ?

To be honest, I never thought before that we, the tutors, are here
to find, fix and repair somebodies' gaps in problems by requests of visitors.

////////////////////////////////

My response to the post by Edwin as @AnlytcPhil

In his post as @AnlytcPhil, Edwin makes a suggestion (= a hypothesis) that the "gap" under your
problem/question is a physical gap on a paper.

As a hypothesis, it is normal.   May be " yes " - may be " no ".

But at the end of his post, Edwin just treats this his hypothesis (= assumption)
as a proven fact, although the proofs were not presented.

Such an arbitrary treatment/replacement of the status " hypothesis "
by the status " the fact " is not acceptable in a fair discussion.

And one more plain explanation at the end.

Edwin, I do not need more explanations about this post.

I simply ask the visitor to place in his future posts only the content of the problem
and do not place nothing else (no one excessive word more), which may lead to misunderstanding.

Answer by greenestamps(13208)   (Show Source): You can put this solution on YOUR website!

5/6 of the mooncakes sold were lotus paste.

let x = # of red bean mooncakes sold
then 5x = # of lotus mooncakes sold

The total number of mooncakes sold is 6x; and half of the mooncakes were sold, so the total number of mooncakes in the bakery at the start was 12x.

The ratio of lotus to red bean mooncakes in the bakery was 3:1, so the number of lotus mooncakes was 9x and the number of red bean mooncakes was 3x.

The original number of red bean mooncakes was 3x, and the number of them sold was x, so the number remaining was 2x. That number remaining was 24, so x is 12.

ANSWER: The number of lotus mooncakes sold was 5x = 60

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = starting number of red cakes
3x = starting number of lotus cakes
x+3x = 4x = starting number of cakes

half of those are sold, so (1/2)*4x = 2x cakes are sold.
5/6 are lotus and 1/6 are red
(1/6)*2x = x/3 red cakes were sold
x-(x/3) = 2x/3 red cakes remain

2x/3 = 24
2x = 24*3
2x = 72
x = 72/2
x = 36 red cakes is what the bakery started with
3x = 3*36 = 108 lotus cakes is what the bakery started with
36+108 = 144 total cakes to start with
0.5*144 = 72 cakes are sold

(5/6)*72 = 60 lotus mooncakes were sold.

Answer by mccravyedwin(408)   (Show Source): You can put this solution on YOUR website!

At a bakery the ratio of the number of lotus paste mooncakes to red bean paste mooncakes was 3 to 1. So there were LP cakes and RB mooncakes and mooncakes to begin with. The shop sold half of the total number of mooncakes. So they sold mooncakes Out of the mooncakes sold, 5/6 were lotus paste. So LP's were sold and RB were sold. In the end there were 24 red bean left. RBs were left so How many lotus paste were sold. Answer = 60 LPs sold. Edwin

Answer by AnlytcPhil(1807)   (Show Source): You can put this solution on YOUR website!

I took that last sentence of this problem differently from the way Ikleyn took it. By this: "Upon question review there is a big gap under the question I do apologise" I assumed that underneath where the problem was written for her assignment, there was a lot of space to write the solution and "fill the gap". That meant that the problem would be difficult and would take a lot of space to write the complete solution. So the student was simply apologizing for asking us to solve a problem that would take a lot of space to write. Edwin

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