Question

One positive number is 5 more than twice another. if their product is 1173, find the numbers.

Answer 1

The numbers are 23 and 51

Explanation:

We have to form equations, let the numbers be x and y,

then,

one positive number is 5 more than twice another

y = 2x + 5 (i)

their product is 1173

(x)(y) = 1173 (ii)

Using (i) in (ii), we get

(x)(2x + 5) = 1173

and solving this,

`x(2x+5)=1173\\2x^2+5x=1173\\2x^2+5x-1173=0\\using / the / quadratic / formula,\\x = (-5 \pm√(5^2-4(2)(-1173)))/2(2) \\the \ squareroot \ gives\\√(25+9384)\\ √(9409) \\= 97\\so, we \ have\\x = (-5 \pm97)/4\\x = 23 \\and\\x = -51/2\\ignoring \ the \ negative \ solution,\\x = 23`

Now, solving for y,

since

(x)(y) = 1173,

y = 117/x

y = 1173/23

y = 51

x = 23