The sum of two numbers is 119. If 4 times the smaller number is subtracted from the larger number the result is nine. Find the two numbers.
The sum of two numbers is 119. If 4 times the smaller number is subtracted from the larger number the result is nine. Find the two numbers.
Call the numbers X (the larger) and Y (the smaller).
X + Y = 119 (line 1)
X – 4Y = 9 (line 2)
X + Y = 119 (line 1)
multiply both sides of line 2 by negative one – (X – 4Y) = –9
–X + 4Y = –9 (line 3)
add line 1 and line 3 5Y = 110
divide both sides by 5 Y = 22 this is the smaller number
substitute 22 for Y in line 1 X + 22 = 119
subtract 22 from both sides X = 97 this is the larger number
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