Question

In a forest 4/7 of all the trees are conifer and the rest are leaf-bearing. Among the leaf-bearing trees 7/15 are oak and 2/3 of these oaks are new. There are 160 old oaks in the forest. How many trees in all are in the forest? (10 marks) The following are two routes of Toronto Transit Commission (TTC) in the Great Toronto Area in Ontario. Kipling Pape Islington a +3 Royal York 3a-2 20 Old Mill Warden Jane In the above diagrams, all the lengths are in miles. It is noticed that the distance from Kipling to Jane=2 times the distance from Pape to Warden. Find an expression, in terms of a, for the distance from Old Mill to Jane. You MUST present your answer in its simplest form. (10 marks) Question 5 Ashdeep and Simranjeet are selling pencils in the student union store in St. Clair College. They sell boxes of pencils and single pencils. Ashdeep sells 7 boxes of pencils and 22 single pencils. Simranjeet sells 5 boxes of pencils and 2 single pencils. I Ashdeep sells twice as many pencils as Simranjeet. You are required to calculate how many pencils are there in a box. (10 marks) Question 6 In a district election in Brampton between two candidates, Joanna Watson and Kate Simpson. Joanna Watson got 55% of the total valid votes and 20% of the total votes were invalid. If the total number of votes was 7,500, the number of valid votes that Kate Simpson got will be? (10 marks) Question 7 In Test 2 of the OAG 160 Business Essential Mathematics, one of your classmates multiplied a number by 3/5 instead of 5/3, What is the percentage error in his calculation ? (10 marks) Question 8 If 75% of a number is added to 75, then the result is the number itself. What is the number? (10 marks) Question 9 405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive? (10 marks) Question 10 Your instructor spends 35% of his income on food, 25% on her daughter's education and 80% of the remaining on a condo in Ajax. What percent of your instructor's income is left with? (10 marks)

Answer 1

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)

`((5)/(3) -(3)/(5) )/((5)/(3) ) *100\%\\\\= (25-9)/(15) (3)/(5) *100\%\\\\=(16)/(25) *100\%\\\\64\%`

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%)

⇒
`(405)/(x) = (20)/(100)x\\ \\(405*100)/(20) = x^(2) \\\\x = \sqrt{(4050)/(2) } \\\\x = 45`

Each child gets x*(20%) sweets

`45(20)/(100) \\\\= 9`

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%