
By: achieve_goal (offline) Saturday, October 27 2012 @ 12:55 AM CDT (Read 1379 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 
Thanks for your help!

Regular Member
Registered: 09/14/11 Posts: 102



