(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
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|
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?
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
