Answer:
Explanation:
Q1) Let T be the total number of trees.
(4/7) T = conifer
⇒ leaf-bearing = T - (4/7) T = (3/7) T
Among the leaf-bearing trees 7/15 are oak
⇒ Oak = (7/15) (3/7) T = (1/5) T
2/3 of these oaks are new.
⇒ 1/3 of these oaks are old
⇒ old oak = (1/3)(1/5) T = (1/15)T
There are 160 old oaks in the forest
⇒ (1/15)T = 160
⇒ T = 160*15 = 2400
There are 2400 trees
Q5)
Let there be x pencils in a box
A = 7x + 22
S = 5x + 2
Also, A = 2S
⇒ 7x + 22 = 2(5x + 2)
⇒ 7x + 22 = 10x + 4
⇒ 10x - 7x = 22 - 4
⇒ 3x = 18
⇒ x = 6
There are 6 pencils in a box
Q6)
Total votes = 7500
20% invalid votes ⇒ 80% valid votes
valid votes = 7500*80% = 6000
Joanna Watson got 55% of the total valid votes
⇒ Kate Simpson got 45% of the total valid votes
K = 6000*45% = 2700 votes
Q7)

Q8)
Let the number be x
x(75%) + 75 = x
⇒ x - x(75%) = 75
⇒ x(25%) = 75
⇒ x = 75*100/25 = 300
Q9)
Let there be x children
Each child receives the same amount of sweet = 405/x
Also, each child receives x*(20%)
⇒

Each child gets x*(20%) sweets

Q10)
Let x be the income
35% x on food
25% x on education
Total expenditure 35% x+ 25% x = 60% x
Remaining income = 40% x
80% on a condo
80% * 40% * x = 32% x
Total spent = 60% x + 32% x = 92% x
Remaining = 8%