Question 147860
Let the two numbers be x & y
:
Write an equation for each statement:
:
"The difference of two numbers is 77."
 x - y = 77
or
 x = (y + 77)
;
" The second is 7 less than 5 times the first."
y = 5x - 7
:
What are the two numbers?
:
Substitute (y+77) for x in the above equation, find y:
y = 5(y+77) - 7
:
y = 5y + 385 - 7
:
y - 5y = 378
:
-4y = 378
y = {{{378/(-4)}}}
y = -94.5 is the 2nd number
:
then
x = -94.5 + 77
:
x = -17.5 is the 1st number
;
:
Check solution in the statement:
"The second is 7 less than 5 times the first."
 -94.5 = 5(-17.5) - 7
 -94.5 = -87.5 - 7; confirms our solutions