Answer:
8 and 6
Step-by-step explanation:
Two numbers are such that their difference, their sum, and their product are to
each other as 1:7:24. Their product must equal what number?
:
Two numbers a & b
Let x = the multiplier
:
a - b = 1x
a + b = 7x
a * b = 24x
:
Add the 1st two equations
a - b = x
a + b = 7x
2a = 8x
a = 4x
or
x = .25a
:
a * b = 24x
Replace 24x; a = 4x therefore:
a * b = 6a
b = 6
;
Using the 1st equation
a - b = 1x
Replace b with 6 and x with .25a
a - 6 = .25a
a - .25a = 6
.75a = 6
a =
a = 8
:
Find the multiplier
a - b = x
8 - 6 = 2
:
Check this
a - b = 2 (1*2)
a + b = 14; (7*2)
a * b = 48: (24*2)
:
The numbers are 8 and 6; their products = 48
Answer:
Width = 3 feet
Length = 7 feet
Step-by-step explanation:
x represents the width of doghouse so,
Width = x
Length is 4 times more than its width
Length = x+4
Area of doghouse = 21 square feet
We know
Area of rectangle = Length * Width
21 = (x+4)*x
21 = x^2+4x
=> x^2+4x-21=0
Solving the above quadratic equation by factorization to find the value of x
x^2+7x-3x-21=0
x(x+7)-3(x+7)=0
(x+7)(x-3)=0
x+7 =0 and x-3=0
x= -7 and x =3
Since the width of rectangle can never be negative so, x=3
Width =x = 3 feet
Length = x+4 = 3+4 = 7 feet
