**Ali, Billy and Caven had some cards. Ali would have twice as many cards as Billy if Billy gave 28 cards to Ali. Both Billy and Caven would have the same number of cards if Caven gave 84 cards to Billy. Given that Caven had 112 more cards than Ali at the beginning, find the number of cards each of them had at the beginning.**

**Solution**

Ali ----- 2 units – 28 (at first)

Billy ----- 1 unit + 28 (at first)

Caven ----- 1 unit + 28 + 84 + 84 (at first)

At first,

(Caven) – (Ali) ---- 112

(1 unit + 28 + 84 + 84) – (2 units – 28) ----- 112

(1 unit + 196) – (2 units – 28) ----- 112

224 – 1 unit ----- 112

224 – 112 ----- 1 unit

1 unit ---- 112

Ali at first

(2 x 112) – 28 = 196

Billy at first

(112) + 28 = 140

Caven at first

(112) + 28 + 84 + 84 = 308

**Answer: Ali had 196, Billy had 140 and Caven had 308**

## 5 comments:

21 scouts crossed a river using a small boat. The boat could carry 3 scouts each time. How many times did the boat cross the river ?

Mr Observer's car departed from Town A and travelled towards Town B. At the same time, his colleague's car started its journey in the direction of Town A from Town B. The two cars passed each other 64 km away from Town B and carried on with their journeys. Both men made an U-turn upon arriving at their own destinations so as to return to their own towns. They passed each other this time 52 km away from Town A. Find the distance between the two places where they passed each other.

Solution:

Base on observer's reference diagram,

C met L on their first journey.

When C moved from their first meeting point and travelled a certain distance to meet L again.

Thus, C has covered 64 km + 64 km from the first meeting point to the second point.

At the second meeting point, C is 52 km away from A. Thus C has also covered 52 + 52 (double distance).

Therefore, 64 x 2 - 52 x2 = 24 km

from both meeting point.

A shopkeeper had some red and blue pens. The number of red pens was 25% of the total number of pens. After selling away 30 red pens and 30 blue pens, the number of red pens became 25% of the number of blue pens left. How many pens did he have at first?

24 Jul 09, 09:14

Worried Soul: Another good start with Priskhipo coming forward to answer qns. Hip Hip Hooray.

24 Jul 09, 09:08

Worried Soul: Good Morning and good start of the day reading Dharma's answers to new questions posted in KSP. Hope that double 'T' may take a short break and let others come forward with a new variety of worked solutions.Also Mrs Wong (NIE trained Sec Sch Teacher) to come forward too.Thanks for all your understanding.

23 Jul 09, 13:23

Worried Soul: What I meant is a short break for both Ts for the time being in order for them to recharge after taking so much effort to solve puppylover's painting problem. In the meantime, pls let others (Mrs Wong-MOE trained current Sec Teacher, Dharma etc)to post their own style of solving methods for all of us (inclusive of 2Ts) to learn. Isn't a good idea and a win-win situation?

thx for this great website my maths improved a lot :D

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