Question 406297
one number divided by 6 is 37 less than another number.
 if the difference between the two numbers is 28, what are the two numbers?
:
Let x = one number
Let y = another number
:
Write an equation for each statement:
:
"one number divided by 6 is 37 less than another number."
{{{x/6}}} = y - 37
Multiply both sides by 6
x = 6(y-37)
x = 6y - 222
:
" if the difference between the two numbers is 28,"
x - y = 28
x = (y+28)
:
Replace x with (y+28) in the 1st equation
y + 28 = 6y - 222
28 + 222 = 6y - y
250 = 5y
y = {{{250/5}}}
y = 50
:
Then
x = 50 + 28
x = 78
:
:
See if that flies in the statement:
"one number divided by 6 is 37 less than another number. "
{{{78/6}}} = 50 - 37
13 = 13, confirms our solutions of x=78. y=50