SOLUTION: The sum of two numbers is 36. The difference between the larger number and 8 equals the total of 4 and 3 times the smaller number. Find the 2 numbers
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Question 102311: The sum of two numbers is 36. The difference between the larger number and 8 equals the total of 4 and 3 times the smaller number. Find the 2 numbers
Answer by doukungfoo(195) (Show Source): You can put this solution on YOUR website!
Lets call the larger number x
and the smaller number y
So first we are told that:
The sum of two numbers is 36
using our variables write an equation to support this statement.
x + y = 36
Ok next we are told that:
The difference between the larger number and 8 equals the total of 4 and 3 times the smaller number.
write an equation to support this statement
x - 8 = 4 + 3y
simplify
x - 3y = 12
ok now we have a system of equations
x + y = 36
and
x - 3y = 12
Lets set the first equation equal to x
x + y = 36
x = 36 - y
Ok so if x equals 36-y we can substitute that into the second equation
x - 3y = 12
36 - y - 3y = 12
36 - 4y = 12
-4y = -24
y = 6
Answer: The smaller number is 6
now we can use this to find the larger number
x + y = 36
x + 6 = 36
x = 30
Answer: The larger number is 30
Check both answers in both equations
x + y = 36
30 + 6 = 36
36 = 36
that works now try the other equation
x - 3y = 12
30 - 3(6) = 12
30 - 18 = 12
12 = 12
That works too.
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