SOLUTION: The sum of two numbers is six less than twice the first number. The first number minus the second number is ten less than four times the second number. What is the smaller number?
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Question 516217: The sum of two numbers is six less than twice the first number. The first number minus the second number is ten less than four times the second number. What is the smaller number?
A. 2
B. 4
C. 6
D. 8
E. 10 Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The sum of two numbers is six less than twice the first number. The first number minus the second number is ten less than four times the second number. What is the smaller number?
:
Let x = the 1st number
Let y = the 2nd number
:
Write an equation for each statement, simplify:
:
"The sum of two numbers is six less than twice the first number."
x + y = 2x - 6
y = 2x - x - 6
y = x - 6
:
"The first number minus the second number is ten less than four times the second number."
x - y = 4y - 10
x = 4y + y - 10
x = 5y - 10
Replace y with (x-6)
x = 5(x-6) - 10
x = 5x - 30 - 10
x - 5x = -40
-4x = -40
x =
x = +10
then
y = 10 - 6
y = 4, the smaller number
:
:
Check solutions in the 2nd statement:
"The first number minus the second number is ten less than four times the second number."
10 - 4 = 4(4) - 10
