(Questions from Yeo Han Ya, 16 Oct 2011)

**1. **
**Sally baked some cookies to sell. 3/4 of them were chocolate cookies and the remaining were almond ****cookies . After she sold 5/6 of chocolate cookies and 210 almond cookies, she had 1/5 of the cookies left. ****How many cookies did she sell?**

My solution:

. Chocolate cookies almond
./ \ / \
|---------|---------|---------|---------|
| | | | | | | 210 |
. \ /
. sold
. / \
| 5u | 5u | 5u | 5u | 5u | 5u | 7u |3u|

"Left" --> 1/5

To even out the number of units from chocolate cookies,

we need to match 8 units with 5 units.

LCM of 8 and 5 is 40, hence the renaming of units above.

7u --> 210

1u --> 210/7 = 30

Total sold --> 5x5u + 7u = (25+7)u = 32x30 =

__960__
Or 5x5u + 210 = 5x5x30 + 210 =

__960__
**2. **

**Jim bought some chocolates and gave half of it to Ken.Ken bought some sweets and gave half of it to Jim. Jim ****ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim's sweets to chocolates became 1:7 and the ratio of**** Ken's sweets to chocolates became 1:4. How many sweets did Ken buy?**

My solution:

The idea:

. ____ 7u_____

. _____ 7u _____ / 4v 18\

. / \ / \/ \

Chox |----------------|----------------|

. Jim Ken

Sweets |----|----|

. \ / \ /

. 12+1u 1v

4v + 18 = 7u

4(12+1u) + 18 = 7u

48 + 4u + 18 = 7u

66 = 3u

1u = 66/3 = 22

No. of sweets Ken bought --> (12+22)x2 = 34x2 = __68__

**3.**

**Shop A has 156kg of rice, while Shop B has 72kg of rice.Each shop sold an equal amount of rice left in their shop ****was 4:1 .Find out how much rice has been sold. **

My solution:

The idea:

. 156kg

. / sold 4u \

Shop A |------|--------------|

.

. sold 1u

Shop B |------|----|

. \ /

. 72kg

This is a constant difference problem (ie. the difference does not change before and after the selling of rice).

We have done this many times before, even during MyPals worksheets.

4u - 1u = 156kg - 72kg

3u = 84kg

1u = 84kg/3 = 28kg

Sold --> 72kg - 28kg = __44kg__