product of two numbers is 75. Find the two numbers if one number is 4 more than twice the other.

Answer 1

x = 4+2y

xy = 75

y = 75/x

x = 4+2(75/x) = 4+150/x

x^2 = 4x + 150

x^2 -4x = 150

complete the square

x^2 -4x +4 = 154

(x-2)^2 = 154

x-2 = +/-sqr154

x = 2+/- sqr154

x = 2+sqr154, or 2-sqr154

y = 75/x

y = 75/(2+sqr154) or 75(2-sqr154)

the two numbers are 2+sqr154 and 75/(2+sqr154)

or 2-sqr154 and 75/(2-sqr154)

either two positive numbers or two negative numbers

Answer 2

Hi Michaela

You can also set up the info directly as given and use the Quadratic Formula to solve for x

Given

xy = 75

One number is 4 more than twice the other, let

y = 2x + 4

Substituting for y in xy = 75 we have

x(2x + 4) = 75

2x² + 4x = 75

Subtract 75 for both sides

2x² + 4x - 75 = 0

We have a quadratic in the form of ax² + bx + c

a = 2, b = 4 c = -75

You can plug these into the Quadratic Formula to solve for x then use the info given in your question to find y

You can look up then Quadratic Formula online or in your text

x = (-b±((b² - 4ac)^1/2))/2a

I got x = 5.205, y = 14.410

and x = -7.205, y = -10,410

Give it a try look up the formula, hope this helps.