A rectangle with sides measuring x in. and 4x-1 in. has an area of 663in.^2. What are the dimensions of the rectangle?

9514 1404 393

  13 in by 51 in

Step-by-step explanation:

The area is the product of the dimensions, so is ...

  663 = x(4x -1)

  4x^2 -x -663 = 0 . . . . . . subtract 663 to put in standard form

Using the quadratic formula, we can find the solutions.

  x = (-(-1) ±√((-1)^2 -4(4)(-663)))/(2(4))

  x = (1 ± √10609)/8 = (1 ±103)/8

Only the positive solution is of any use in this problem, so ...

  x = 104/8 = 13

  4x-1 = 4(13)-1 = 51

The dimensions of the rectangle are 13 inches by 51 inches.

__

I find it easiest to solve these using a graphing calculator.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: