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Sagot :
i ) 3(2x - 3) = 4(2x + 4)
[tex]6x - 9 = 8x +1 6 \\ \\ 6x - 8x = 16 + 9 \\ \\ - 2x = 25 \\ \\ x = - \frac{25}{2} .[/tex]
ii )2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
[tex]2x + 4 + 5x + 25 = 4x - 32 + 2x - 4 \\ \\ 7x + 29 = 6x - 36 \\ \\ 7x - 6x = - 36 - 29 \\ \\ x = - 65.[/tex]
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2. 3x /4 - 7 /4 = 5x + 12
[tex] \frac{3x}{4} - \frac{7}{4} = 5x + 12 \\ \\ \frac{3x}{4} - 5x = 12 + \frac{7}{4} \\ \\ \frac{3x - 20x}{4} = \frac{48 + 7}{4} \\ \\ \frac{ - 17x}{4} = \frac{55}{4} [/tex]
cancel 4 from both sides
[tex] - 17x = 55 \\ \\ x = \frac{ - 17}{55} .[/tex]
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3. x +7 - 8x/3 = 17/6 - 5x/8
[tex]x + 7 - \frac{8x}{3} = \frac{17}{6} - \frac{5x}{8} [/tex]
put x = 4
[tex]4 + 7 - \frac{ 8\times 4}{3} = \frac{17}{6} - \frac{5 \times 4}{8} \\ \\ 11 - \frac{32}{3} = \frac{17}{6} - \frac{20}{8} \\ \\ \frac{33 - 32}{3} = \frac{68 - 60}{24} \\ \\ \frac{1}{3} = \frac{8}{24} \\ \\ \frac{1}{3} = \frac{1}{3} .[/tex]
L.H.S. = R.H.S.
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4. Let 3 consecutive integers : x , x+1 , x+2
As per the question : 2x + 3(x+1) + 4(x+2) = 56
9x + 11 = 56
Transpose 11 to RHS
9x = 45
Divide both sides by 9
x = 5 ,
x + 1 = 5 + 1 = 6
x + 2 = 5 + 2 = 7
Numbers are 5 , 6 and 7 .
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5. Let the age of Jane’s younger sister is x.
Age of Jane will be x + 6
As per the question, after 10 years the sum of their ages will be 50.
After 10 years,
age of Jane = x + 16
age of her younger sister = x + 10
Therefore,
x + 16 + x +10 = 50
2x + 26 = 50
2x = 24
x = 12
Thus, the present age of Jane’s younger sister is 12 years.
And of Jane’s is 12 + 6 = 18 years.
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6. Let the breadth of rectangular swimming pool be x metres.
Then, its length = (2x + 2) metres.
We know that the Perimeter of a rectangle
= 2(Length + Breadth)
= 2(2x + 2 + x) = 6x + 4
According to the given condition, we have
6x + 4 = 154
6x = 154 − 4
6x = 150
[Dividing both sides by 6]
x = 25
Thus, breadth = 25 m and
length = 25 × 2 + 2 = 52 m .
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7. Let the digit in ten's .
Place be x and the digit in the one's place be y.
x − y = 5 ⟶ (i)
Two digit number = 10x + y
Two digit after reversing the digits = 10y + x
According to question ,
10x + y + 10y + x = 99
11x + 11y = 99
x + y = 9 ⟶ (ii)
On adding (i) and (ii),
2x = 14
x = 7
Putting the value of x in equation (i)
x − y = 5
y = 2
Number = 10x + y
=72 .
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8. Let the speed of the steamer in still water be x km/h.
Then , the speed downstream = (x+2) km/h
and the speed upstream = (x−2) km/h
Given , distance covered in 4 hours downstream = distance covered in 5 hours upstream
4(x + 2) = 5(x − 2)
4x + 8 = 5x − 10
4x − 5x = − 10 − 8
[Transposing 5x to LHS and 8 to RHS]
−x = −18 or x = 18 km/h .
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9. Let the number of notes of different denomination be x.
∴ Numbers of Rs 100 notes , 50 notes and Rs 10 notes will be 2x , 3x and 5x respectively.
Amount of 100 Rs notes ⇒Rs 100 × 2x = 200x
Amount of 50 Rs notes ⇒Rs 50 × 3x = 150x
Amount of 10 Rs notes ⇒Rs 10 × 5x = 50x
As per the question
Total amount = 400000
200x + 150x + 50x = 400000
400x = 400000 , x = 1000
No of Rs 100 notes = 2x = 2 × 1000 = 2000
No of Rs 50 notes = 3x = 3 × 1000 = 3000
No of Rs 10 notes = 5x = 5 × 1000 = 5000 .
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10. Let the age of the man be x
Then age of his son becomes (x − 24)
2 years later from now,
Age of man will be = x + 2
and age of his son will be = (x − 24 + 2) = x − 22
According to question,
2(x − 22) = x + 2
i.e., 2x − 44 = x + 2
i.e., x = 46
Therefore ,
Present age of man = 46 years
And present age of his son = 46 − 24 = 22 years .
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