SOLUTION: 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

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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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2F7
y = 66%2F7; the 2nd number
:
Find x:
x = 2y - 7
x = 2(48%2F7 - 7
x = 96%2F7 - 49%2F7
x = 47%2F7
x = 65%2F7; 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%2F7 + 20 = 4(47%2F7)
48%2F7 + 140%2F7 = 188%2F7
188%2F7 = 188%2F7; confirms our solutions