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Exercise 8.5
Q9:
6
x−4 =
5
x+7
Cross-multiplying the fractions, we get
6(x+ 7) = 5(x− 4)
6x+ 42 = 5x− 20
6x− 5x = −42− 20
x = −62
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Q17:
1
x −
8
21 =
3
7x
The Least Common Multiple (LCM) of all the denominators is 21x. So we
convert all of them to 21x.
21
21x −
8x
21x =
9
21x
Canceling the common denominator,
21− 8x = 9
8x = 12
x = 128 =
3
2
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Q19:
5
x−6 − 5 =
2x
x−6
Taking LCM = 5(x-6),
5−5(x−6)
x−6 =
2x
x−6
Canceling the common denominator,
5− 5x+ 30 = 2x
7x = 35
x = 5
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Q23:
1
3 +
1
x+4 =
1
x
Taking LCM of the Left Hand Side of equation,
x+4+3
3(x+4) =
1
x
x+7
3(x+4) =
1
x
Cross-multiplying the fractions,
x(x+ 7) = 3(x+ 4)
1
x2 + 7x = x+ 12
x2 + 4x− 12 = 0
Breaking the quadratic term into factors,
x2 + 6x− 2x− 12 = 0
Grouping the first two terms and last two terms,
x(x+ 6)− 2(x+ 6) = 0
(x− 2)(x+ 6) = 0
x = 2 or x = −6
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Q29:
6
x−3 + 1 =
2x
x−3
Taking the LCM = x-3,
6+(x−3)
x−3 =
2x
x−3
x+ 3 = 2x
x = 3
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Q35:
2
4x−1 +
1
x+1 =
3
x+1
Taking LCM of left hand side of equation,
2(x+1)+(4x−1)
(4x−1)(x+1) =
3
(x+1)
Cancelling out(x+1) term from both sides and cross-multiplying,
2x+ 2 + 4x− 1 = 3(4x− 1)
6x+ 1 = 12x− 3
6x = 4
x = 46 =
2
3
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Q45:
Price Tax
$ 1 6 cents
$ x 51 cents
The table explains the data available. Cross-multiplying will give the value of
x.
1× 51 = 6× x
x = 516
x = $8.5
2
Thus the price of the item is $8.5 if sales tax is 51 cents.
———————————————————————————
Q47:
Bulbs produced Defective
$ 100 3
$ 4800 x
The table explains the data available. Cross-multiplying will give the value of
x.
100× x = 3× 4800
x = 3× 48 = 144
if the daily production is 4800 bulbs, 144 of them will be defective.
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Q51:
Hits At Bat
$ 17 50
$ 204 x
The table explains the data available. Cross-multiplying will give the value of
x.
17× x = 50× 204
x = 50×20417 = 600
Thus Pete will need 600 ”at bats” to get 204 hits.
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Q55:
Object Actual Length Shadow Length
Man 6 ft 4.5 ft
Flag-post x 30 ft
The table explains the data available. Cross-multiplying will give the value of
x.
6× 30 = x× 4.5
x = 6×304.5 = 40
Thus the actual length of the flag-post if 40 ft.
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Exercise 8.6
Q1:
x
y
=
7
9
(1)
x+ y = 48 (2)
3
Using equation (1),
x = 7y9
Putting this in (2),
7y
9 + y = 48
7y+9y
9 =...