Question 120636
Write an equation for each statement:
:
"One number is 16 more than another."
Smaller number = x
one number = (x+16)
: 
"If the smaller number is subtracted from two thirds of the larger number, the result is one fourth of the sum of the two numbers."
{{{2/3}}}(x+16) - x = {{{1/4}}}((x+16) + x)
:
{{{2/3}}}(x+16) - x = {{{1/4}}}(2x+16)
:
Multiply equation by 12:
12*{{{2/3}}}(x+16) - 12*x = 12*{{{1/4}}}(2x+16)
Cancel out the denominators and you have:
:
4(2)(x+16) - 12x = 3(2x+16)
8(x+16) - 12x = 6x + 48
8x + 128 - 12x = 6x + 48
:
8x - 12x - 6x = 48 - 128
-10x = -80
x = {{{(-80)/(-10)}}}
x = + 8
and
8 + 16 = 24 is the larger number
:
:
Check solution in the statement:
"If the smaller number is subtracted from two thirds of the larger number, the result is one fourth of the sum of the two numbers."
 {{{2/3}}}*24 - 8 = {{{1/4}}}(24+8)
16 - 8 = {{{1/4}}}*32
 8 = 8 confirms our solutions
:
Did I make this clear to you? Let me know please, any questions?