If $3 a + 2 b = 24$ and $4 a + 5 b = 53$ , calculate the value of $a + b$ .

2

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7

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9

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11

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Solution

The correct option is D $11$
Let $\Rightarrow 3 a + 2 b = 24$ ........eq(1)
$\Rightarrow 4 a + 5 b = 53$ ........eq(2)
Multiply the eq(1) by $5$ and eq(2) by $2$ , we get
$\Rightarrow 15 a + 10 b = 120$ .....eq(3)
$\Rightarrow 8 a + 10 b = 106$ ....eq(4)
Subtract the eq(3) and eq(4), we get
$\Rightarrow 7 a = 14$
$\Rightarrow a = \frac{14}{7} = 2$
Substitute the value if in eq(1)
$\Rightarrow 3 \times 2 + 2 b = 24$
$\Rightarrow 6 + 2 b = 24$
$\Rightarrow 2 b = 24 - 6$
$\Rightarrow 2 b = 18$
$\Rightarrow b = \frac{18}{2} = 9$
$∴ a + b = 2 + 9 = 11$

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