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 By: achieve_goal (offline)  Saturday, October 27 2012 @ 12:55 AM CDT (Read 1399 times)
achieve_goal

Mrs Lim baked some tarts. She packed all tarts in either small or big boxes. She packed 7 tarts in each small box and 10 tarts in each big box. At first, there were 4 times as many small boxes as the big boxes. After selling half of the number of small boxes and some big boxes of tarts, Mrs Lim gave her friends another 8 small boxes of tarts. The number of tarts in the unsold small boxes was thrice the number of tarts in unsold big boxes. There were 280 tarts left in the big and small boxes. How many tarts did Mrs Lim bake at first?

Pls help!

Regular Member

Registered: 09/14/11
Posts: 102

 By: echeewh (offline)  Saturday, October 27 2012 @ 08:29 AM CDT
echeewh

Hey there,

Following pls find my worked solution:

<Before>
Ratio (of boxes)
S : B
4 : 1

Number of tarts: (use <Number x Value> method)
S:
4u × 7 = 28u

B:
1u × 10 = 10u

<process>
(1/2) of S sold; 8S given away; some B sold;
S:
14u + (8 × 7) = 14u + 56

<after>
Ratio (of tarts)
S : B
3 : 1

S:
28u - 14u - 56 = 14u - 56

B:
[(14u - 56) / 3]

Given that S + B = 280 tarts, we have ...

14u - 56 + [(14u - 56) / 3] = 280

Multiply whole equation 3x:

3 × (14u - 56) + 14u - 56 = 3 × 280
42u - 168 + 14u - 56 = 840
56u --> 840 + 168 + 56
56u --> 1064
1u --> 19

Number of tarts baked (at first) = 28u + 10u = 38u

Hence, 38u --> 38 × 19 = 722 tarts

=============================

Trust this helps

Do let me know again if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: hci (offline)  Saturday, October 27 2012 @ 09:47 AM CDT
hci

Alternatively, you can use this method.

The number of tarts left were 280, so 3u from small boxes, 1u from big boxes, hence 280 divide by 4 to get the number of 1u. since 1 u =70 tarts, number of tarts from small boxes remain will be 70x3=210 tarts

210 tarts is after she sold half of the small boxes and gave away (7x8=56 tarts to her friends)
hence you add 56 to 210 to get half of the small boxes which is 266 tarts.

266 x 2 =532 is the total number of tarts in the small boxes

532 divide by 7 =76 to get the number of small boxes

76 divide by 4 =19 to get the number of big boxes.
Number of tarts in big boxes = 19 x10
=190
so total number of tarts she baked were 190 + 532 = 722 tarts

Hope this helps!

Newbie

Registered: 05/10/11
Posts: 3

 By: achieve_goal (offline)  Monday, October 29 2012 @ 04:11 AM CDT
achieve_goal