Venn diagrams Answers AWS
Venn diagrams Answers GCSE Mathematics FP6/8 HP6/8/9 1. One Saturday morning Kay serves 84 customers at her café. Her customers buy food or drinks or both. Complete the following Venn diagram knowing that a 2/3 of her customers buy drinks and 75% of her customers buy food. F = customers that buy food D = customers that buy drinks Answer: D
F
28 .......
35 .......
2 of 84 = 84 3 75% of 84 = 84
21 .......
3 x 2 = 56 4 x 3 = 63
Food and Drink = 56 + 63 - 84 = 35 Drink only = 56 - 35 = 21 Food only = 64 - 35 = 28
2. Alyson is arranging her works Christmas meal for 60 people at a local restaurant. All guests must order a main meal and there is the option to add a starter and/or a dessert. • 25 people order a starter, • 39 people order a dessert • 17 people order both a starter and a dessert. (a) Show this information on a Venn diagram. S = people that order a starter D = people that order a dessert D
S
8 .......
13 .......
17 .......
22 .......
Answer: Starter only = 25 - 17 = 8 Dessert only = 39 - 17 = 22 No starter or dessert = 60 - 8 - 17 - 22 = 13
Venn diagrams Answers GCSE Mathematics FP6/8 HP6/8/9 (b) Knowing that the restaurant charges £15 for 1 course, £18 for 2 courses and £20 for 3 courses, find the total cost of the Christmas party.
Answer:
1 course = 13 x 15 = 150 + 45 = £195 2 course = ( 8 + 22 ) x 18 = £540 3 course = 17 x 20 = £340
195 540 + 340 1075
Higher Tier Only
3.
Guests at Hotel Playa in Malaga Spain are asked if they speak English, French or Spanish. Of the 120 guests: • 78 speak English, 49 speak French and 69 speak Spanish • 40 speak English and Spanish • 11 speak English and French • 33 speak French and Spanish • 8 speak all three languages
(a) Show this information in a Venn diagram S
E
35
32
4
8 3
25
Answer: 35 + 32 + 25 + 13 + 8 + 4 + 3 = 120
13
F
(b)
A guest is chosen at random to dine with the hotel Manager at the Gala dinner. What is the probability that the guest speaks Spanish but not English? Answer: 29 120
F
28 .......
35 .......
2 of 84 = 84 3 75% of 84 = 84
21 .......
3 x 2 = 56 4 x 3 = 63
Food and Drink = 56 + 63 - 84 = 35 Drink only = 56 - 35 = 21 Food only = 64 - 35 = 28
2. Alyson is arranging her works Christmas meal for 60 people at a local restaurant. All guests must order a main meal and there is the option to add a starter and/or a dessert. • 25 people order a starter, • 39 people order a dessert • 17 people order both a starter and a dessert. (a) Show this information on a Venn diagram. S = people that order a starter D = people that order a dessert D
S
8 .......
13 .......
17 .......
22 .......
Answer: Starter only = 25 - 17 = 8 Dessert only = 39 - 17 = 22 No starter or dessert = 60 - 8 - 17 - 22 = 13
Venn diagrams Answers GCSE Mathematics FP6/8 HP6/8/9 (b) Knowing that the restaurant charges £15 for 1 course, £18 for 2 courses and £20 for 3 courses, find the total cost of the Christmas party.
Answer:
1 course = 13 x 15 = 150 + 45 = £195 2 course = ( 8 + 22 ) x 18 = £540 3 course = 17 x 20 = £340
195 540 + 340 1075
Higher Tier Only
3.
Guests at Hotel Playa in Malaga Spain are asked if they speak English, French or Spanish. Of the 120 guests: • 78 speak English, 49 speak French and 69 speak Spanish • 40 speak English and Spanish • 11 speak English and French • 33 speak French and Spanish • 8 speak all three languages
(a) Show this information in a Venn diagram S
E
35
32
4
8 3
25
Answer: 35 + 32 + 25 + 13 + 8 + 4 + 3 = 120
13
F
(b)
A guest is chosen at random to dine with the hotel Manager at the Gala dinner. What is the probability that the guest speaks Spanish but not English? Answer: 29 120
