Foundation November 2017 Paper 3 Q16
16
(a) Two bags each contain only red counters and yellow counters.
In Bag A, the ratio of red counters to yellow counters is 1 : 4.
In Bag B, \(\dfrac{1}{4}\) of the counters are red.
(i) Sharon says
The proportion of the counters that are red is the same in both bags.
Explain why Sharon is not correct. [1]
(ii) The number of counters in the two bags is the same.
Complete the table below to show how many counters of each colour could be in the bags.
| Red counters | Yellow counters | |
|---|---|---|
| Bag A | ||
| Bag B |
[3]
(b) In another bag, Bag C, the ratio of red counters to yellow counters is 3 : 4.
If 3 of the red counters are removed from Bag C, the ratio of red counters to yellow counters is 3 : 5.
If 3 of the red counters are removed from Bag C, the ratio of red counters to yellow counters is 3 : 5.
How many yellow counters are in Bag C? [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) \(\dfrac{1}{5}\) of Bag A’s counters [are red] or The ratio of red to yellow in Bag B is 1:3 | 1 | Accept 1 : 4 = \(\dfrac{1}{5}\) Accept \(\dfrac{1}{4}\) = 1 : 3 | Equivalents may be percentages or decimals Eg. Bag A: 20% red, Bag B: 25% red. |
| (ii) Correct answer is any integer multiple of this. Bag A: Red 4, Yellow 16 Bag B: Red 5, Yellow 15 | 3 | B1 for (Bag A) yellow = 4 \(\times\) red and A total = B total B1 for (Bag B) yellow = 3 \(\times\) red If 0 scored SC2 for correct figures but transposed horizontally | Eg \(\times\)2: 8, 32 and 10, 30 \(\times\)3: 12, 48 and 15, 45 \(\times\)4: 16, 64 and 20, 60 \(\times\)5: 20, 80 and 25, 75 \(\times\)6: 24, 96 and 30, 90 \(\times\)10: 40, 160 and 50, 150 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 20 nfww | 3 | B1 for two ratios equivalent to 3:4 M1 for their 15:20 reduced to (15-3):20 Alternative approach B1 for two fractions equivalent to \(\dfrac{3}{7}\) M1 for their \(\dfrac{15}{35}\) reduced to \(\dfrac{15 - 3}{32}\) | 6:8, 9:12, 12:16, 15:20,… their 15:20 any ratio but not 3:4 using equivalent fractions: Eg \(\dfrac{6}{14}\) or \(\dfrac{9}{21}\) or \(\dfrac{12}{28}\) or \(\dfrac{15}{35}\) their \(\dfrac{15}{35}\) any fraction but not \(\dfrac{3}{7}\) |