Six hundred minus three fourths of a number is three times the number. Find one fourth of the number.

Question

solve this at your highest speed

Answer 1

To find this at "highest speed" (not necessarily, most understandable),

             let N=the number, y =N/4; find y.

 

600 - (3/4)N = 3N           (write the given equation)

600 - (3/4)(4y) = 3(4y)         (put in 4y for N)

600 -3y = 12y                  (cancel 4's and multiply 3*4)

600 = 15y                    (add 3y to both sides)

40 = y           (answer, we found one fourth of the number)

 

Answer 2

Let x = a number

 

The term "is" means equal.  This tells us to write an equation.

 

 

600 - (3/4)x = 3x

 

 

Our equation has a denominator.  Rewrite the equation using the LCD.  LCD is 4.

 

(2400 - 3x) / 4 = 12x / 4

 

 

Since the denominators are the same, we only need to equate numerators.

 

2400 - 3x = 12x

 

 

Add 3x on both sides of equation.

 

2400 = 15x

 

 

Divide both sides of equation by 15.

 

 

x = 160

 

 

The number is 160.  Now the question asks for one fourth of the number.

 

Divide this number by 4.  This is the same as multiplying by 1/4.

 

 

160 / 4 = 40

 

 

The number we truly want is 40.