Question 408092
i think of a pair of numbers.
if i add 7 to the first.i obtain a number which is twice the second if i add 20 to the second.i obtain a number which is four times the first.what are the numbers?
:
Two numbers, x & y
:
"I think of a pair of numbers, If I add 7 to the first, I obtain a number which is twice the second"
x + 7 = 2y
x = (2y-7)
:
"If I add 20 to the second, I obtain a number which is four times the first."
4x = y + 20
Replace x with (2y-7)
4(2y-7) = y + 20
8y - 28 = y + 20
8y - y = 20 + 28
7y = 48
y = {{{48/7}}}
y = 6{{{6/7}}}; the 2nd number
:
Find x:
x = 2y - 7
x = 2({{{48/7}}} - 7
x = {{{96/7}}} - {{{49/7}}}
x = {{{47/7}}}
x = 6{{{5/7}}}; the 1st number
:
:
Check solutions in the statement:
"If I add 20 to the second, I obtain a number which is four times the first."
{{{48/7}}} + 20 = 4({{{47/7}}}) 
{{{48/7}}} + {{{140/7}}} = {{{188/7}}}
{{{188/7}}} = {{{188/7}}}; confirms our solutions