Question

Three times a no. And five times another no. Give 169.five times the first no.and three times the second no. Gives 159 ?find the no.?

Answer 1

Step-by-step explanation:

let two numbers be x and y

according to question,

$3x + 5y= 169 \: \: \: \: \: \: \: \: \: \: \: \: \: ......(1) \\ and \\ 5x + 3y = 159 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .......(2) \\ equation \: (1) \times 3 - equation \: (2) \times 5 \\ 9x - 25x + 15y - 15y = 507 - 795 \\ - 16x = - 288 \\ x = \frac{ - 288}{ - 16} \\ x = 18 \\ put \: the \: value \: of \: x \: in \: equation \: (1) \\ 3 \times 18 + 5y = 169 \\ 54 + 5y = 169 \\ 5y = 169 - 54 \\ 5y = 115 \\ y = \frac{115}{5} \\ y = 23 \\ \\ hence \: two \: numbers \: are \: 18 \: and \: 23.$

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