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?

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

RELATED QUESTIONS
The sum of two numbers is six less than twice the first number. When the second number is (answered by ankor@dixie-net.com)

The sum of two numbers is 51. The second number is six less than twice the first number.... (answered by rfer)

the sum of two numbers is 75. the second number is 3 less than twice the first. find the... (answered by ewatrrr)

The sum of two numbers is 23 less than twice the first number. Their difference is 19... (answered by dfrazzetto)

The sum of two numbers is 75. The second number is 3 less than twice the first. Find the... (answered by amoresroy)

the sum of two numbers is 75. The second number is 3 less than twice the first. fine the... (answered by solver91311)

the sum of two numbers is 75. the second number is 3 less than twice the first. find the... (answered by powercenter)

the sum of three numbers is 150. The second number is thrice the first, and the third is... (answered by jorel1380)

The sum of two numbers is 15 less than twice the first number. Their difference is 5 less (answered by Paul)