# Question

On a particular day, Mary baked an equal no of lemon & cheese tarts for sale. For every lemon tart sold that day, 2 cheese tarts were sold. In the morning, she sold 3/5 of the tarts she baked. She then sold 1/4 of the remaining cheese tarts in the afternoon and had 12 cheese tarts left.

a) how many lemon tarts did she sell in the morning?

b) how many tarts did she bake altogether.

TIA.

12/3 = 4

4×4 = 16

Assume that there were 5 units of lemon tarts and 5 units of cheese tarts at first.

1 unit of lemon tarts and 2 units of cheese tarts were sold in the morning. Hence left with 4 units of lemon tarts and 3 units of cheese tarts.

1u = 16

16 x 2 = 32 lemon tarts sold in the morning

b) 16 x 10 = 160

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What was left in the end was 12 “cheese” tarts. 12 is not total of what’s left…

That’s what I have right?

Mary had  3u cheese tarts left after selling 12u in the morning.

She then sold 1/4 of 3u, and had 3/4 of 3u left.

3/4 of 3u = 9/4 u

9/4 u = 12

1u = 16/3

Makes for a cleaner solution, and the 1u in the end is not a fraction.

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I would solve the above question as follows :

2 x 5 x 4 = 40
40u/2 = 20u (of lemon and cheese tarts each)
(3/5) x 40u = 24u
24u/3 = 8u (lemon tarts sold in the morning)
8u x 2 = 16u or 24u – 8u = 16u (cheese tarts sold in the morning)
20u – 16u = 4u
(1/4) x 4u = 1u (cheese tarts sold in the afternoon)
4u – 1u = 3u ——- 12
1u ——- 12/3 = 4
4 x 8u = 32 (a)
4 x 40u = 160 (b)

Ans : (a) 32 lemon tarts; (b) 160 tarts.

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 Lemon Cheese Total At First 30u 30u 60u sold 12u 24u 36u (3/5 of 60u) Left b4 afternoon 18u 6u 24u

3/4 of 6u = 4.5u
4.5u =12
u = 8/3

a) Lemon tart sold = 12u = 12 X 8/3 = 32 tarts ##
b) Altogether she bakes = 60u = 60 x 8/3 = 160 tarts ##

How do we know it was 30u each at 1st? Thanks.

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I would use the LCM of 5 and 4 since she is selling 5 units in the morning and going to sell 1/4 of the remainder.

Given that she sold 3/5 of the total, and the tarts are in ratio of 1 : 2, we can break 3/5 into 1/5 and 2/5.

There is an equal number of each tart, 20u + 20u = 40u.

1/5 = 8/40
2/5 = 16/40

Using LCM method will bypass those recurring numbers.

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We have this info, she baked the same qty for both.  A convenient total ‘u’ would be divisible by 2, so lemon and cheese can have equal share. Next we were told she sold 3/5 of the total. I have to consider that the total has to be divisible by 5. So I can get 3/5 of 60 as 36.

Basically I am looking for common multiple of 2 and 5 to use for the total in the beginning.

You can use 10u, 30u (use by Bigdevil) or 60u use by me.  Or 100u if you want. All will work.

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This is a Matrix question.

LCM of 4 and 5 is 20

1/5 = 8/40

2/5 = 16/40

 Morning Afternoon Left Total Lemon 8u 12u 20u Cheese 16u 1u 3u 20u Total 40u

3u = 12

1u = 12 ÷ 3= 4

a) 8u = 8 × 4 = 32

b) 40u = 4 × 40 = 160

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