One number is three more than the other number. When the square of the smaller number is subtracted from the square of the smaller number, #45# is obtained. What are the two numbers?

3 Answers
Mar 23, 2017

Let the numbers be #x# and #y#.

#{(x + 3 = y), ((x + y)(y - x) = 45):}#

If we rearrange the first équation, we get #x - y = 3#. Substituting, we get:

#(x + (x + 3))(3) = 45#

#2x + 3 = 15#

#2x = 12#

#x = 6#

#:.#The numbers are #6# and #9#.

Hopefully this helps!

Mar 23, 2017

Answer:

I got #6 and 9#

Explanation:

let s call our numbers #x# and #y#. We get:
#x=y+3#
and
#(x+y)(x-y)=45#
from the second we get:
#x^2-y^2=45#
substituting the first equation #x=y+3# we get:
#(y+3)^2-y^2=45#
#y^2+6y+9-y^2=45#
#6y=36#
#y=36/6=6#
so that #x=6+3=9#

Mar 23, 2017

Answer:

The first number is 9, and the second number is 6.

Explanation:

Let #n# be the first number. The second number is therefore #n-3#.

Sum of the numbers: #color(red)((n)+(n-3) = 2n-3)#
Difference of the numbers: #color(blue)((n)-(n-3) = 3)#

Equation:
#color(red)((2n-3))color(blue)((3))=45#

#2n-3=15#

#2n=18#

#n=9# (First number)
#n-3=6# (Second number)