2 word problems i really need help on

Question

1. if the sum of two numbers is 1 and their product is -56. find the two numbers

 

 

2. the longer leg of a right triangle is 4 feet longer than the other leg. Find the length of the two legs if the hypotenuse is 20 ft.

Answer 1

Question 1

 

Let x = one number

Let y = another number

 

x + y = 1         eq1

xy = -56           eq2

 

 

Substitute eq1 into eq2.

 

x(1 - x) = -56

 

x - x² = -56

 

Subtract x and subtract x² on both sides equation.  We do this so we can have a positive x² term, allowing us to factor using FOIL and spear us time on using the quadratic formula if possible.

 

0 = x² - x - 56

0 = (x + 7)(x - 8)

 

x = -7      and       x = 8

 

 

Substitute these values into eq2.

 

y = -56/(-7)          and         y = -56/8

y = 8                    and          y = -7

 

 

Our numbers are:

 

-7 and 8  because their sum is 1 and the their product is -56.

 

 

Question 2

 

Let one leg = x

Let longer leg = x + 4

Hypotenuse = 20

 

Use the Pythagorean theorem, since we have a right triangle.

 

x² + (x + 4)² = 20²

x² + (x² + 8x + 16) = 400

2x² + 8x - 384 = 0

 

Factor out the GCF on the left side of equation.

 

2(x² + 4x - 192) = 0

2(x - 12)(x + 16) = 0

 

x = 12    and   x = -16

 

We accept the positive value of x. Substitute the positive value of x into our dimensions.

 

One leg = 12 ft

The longer leg = 16 ft

 

Let's check these values.

 

12² + 16² = 20²

144 + 256 = 400

400 = 400

 

It checks out.