Question

3. There are two numbers such that the
sum of twice the first number and
thrice the second number is 141 and
sum of thrice the first number and
twice the second number is 174.
Which is the largest number?

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Answer 1

Step-by-step explanation:

let the two numbers be x and y

according to the condition 1

$2x + 3y = 14$

according to the condition 2

$3x + 2y = 174$

now solve it,

$from \: eqn \: {1} \:$

$x = \frac{14 - 3y}{2} \\ \\ put \: it \: in \: eqn \: 2$

$3 \times \frac{14 - 3y}{2} + 2y = 174 \\ \frac{42 - 9y}{2} + 2y = 174 \\ 42 - 9y - 4y = 174 \\ - 13y = 174 - 42 \\ - 13y = 132 \\ y = - \frac{132}{13}$

now put y=-132/13 in eqn (1)

$2x + 3 \times \frac{ - 132}{13} = 14 \\ 2x - \frac{396}{13} = 14 \\ 26x - 396 = 182 \\ 26x = 182 + 396 \\ 26x = 578 \\ x = 578 \div 26 \\ x = 22.23$

hence x is largest

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