[5 marks sum]

Question 15 Marks

Solve the following equation $: (7y + 8) + 7= 8$

Answer

$(7y +8) +7= 8$
$\Rightarrow \frac{7 y+8}{7}=8$
$\Rightarrow \frac{7 y+8}{7} \times 7=8 \times 7 \ldots($ Multiplying by $7)$
$\Rightarrow 7 y+8=56$
$\Rightarrow 7 y+8-8-56-8 \ldots($ Subtracting $8$ from both sides $)$
$\Rightarrow 7 y=48$
$\Rightarrow \frac{7 y}{7}=\frac{48}{7} . .($ Dividing by $7)$
$\Rightarrow y=\frac{48}{7}=6 \frac{6}{7}$

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Question 25 Marks

The sum of three consecutive numbers is 54. Taking the middle number as x, find:

(i) expression for the smallest number and the largest number.

(ii) the three numbers.

Answer

Sum of three consecutive numbers = 54
Middle number = x
(i) The first number = x – 1
and third number = x + 1
(ii) ∴x + x-1+x+1 = 54
⇒ 3x = 54
$\Rightarrow x=\frac{54}{3}=18$
∴ First number =18 - 1 = 17
and third number =18 + 1 = 19
∴ Three required numbers are 17, 18,19

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Question 35 Marks

Find three consecutive integers such that their sum is 78.

Answer

Sum of three consecutive numbers = 78
Let first number = x
Then second number = x + 1
and third number = x + 2
Then x + x+1+x + 2 = 78
⇒ 3x + 3 = 78
⇒ 3x = 78 – 3 = 75
$\Rightarrow x=\frac{75}{3}=25$
∴ First number=25
Second number = 25 + 1 = 26
and third number = 26 + 1 = 27
Then the three required numbers are 25, 26, 27

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Question 45 Marks

When three consecutive natural numbers are added, the sum is 66, find the numbers.

Answer

Let first natural number = x
Then second natural number = x + 1
and third number = x + 2
According to the sum,
x + x + 1 + x + 2 = 66
⇒ 3x + 3 = 66
⇒ 3x = 66 - 3 = 63
$\Rightarrow x=\frac{63}{3}=21$
∴ First natural number = 21
second number = 21 + 1 = 22
and third number = 22 + 1 = 23
Hence numbers are 21, 22, 23

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MATHS [5 marks sum]

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