SOLUTION: Twice the larger of the two numbers is three more than five times the smaller, and then the sum of four times the larger and three times the smaller is 71. What are the nos.?

Question 120139: Twice the larger of the two numbers is three more than five times the smaller, and then the sum of four times the larger and three times the smaller is 71. What are the nos.?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = the larger number
Let y = the smaller number
:
Write an equation for what it says:
:
"Twice the larger of the two numbers is three more than five times the smaller,"
2x = 3 + 5y
Or
2x - 5y = 3
:
"and then the sum of four times the larger and three times the smaller is 71."
4x + 3y = 71
:
What are the nos.?
:
Multiply 2x+3y=3, by 2, and subtract 4x+3y=71 from it
4x - 10y = 6
4x + 3y = 71
--------------- subtracting eliminate x; find y
0x - 13y = -65
y =
y = +5
:
Find x using the 1st equation
2x = 3 + 5(5)
2x = 3 + 25
2x = 28
x = 14
The two numbers are 14 and 5
:
Check solution in the statement:
the sum of four times the larger and three times the smaller is 71.
4(14) + 3(5) = 71
RELATED QUESTIONS
twice the larger of two numbers is three more than five times the smaller and the sum of... (answered by stanbon)

Twice the larger of two numbers is three more than five times the smaller and the sum of... (answered by mananth)

Twice the larger of two numbers is three more than five times the smaller, and the sum... (answered by jorel555,MathTherapy)

Twice the larger of two numbers is three more than five times the larger and three times... (answered by stanbon)

Twice the larger number of 2 numbers is 3 more than five times the smaller.And the sum of (answered by josgarithmetic)

Three times the larger of the two numbers is 10 more than twice the smaller. Five times... (answered by ankor@dixie-net.com)

The larger of two numbers is one more than twice the smaller. The sum of the numbers is... (answered by mananth)

The larger of two numbers is 8 more than twice the smaller. The sum of the numbers is 10... (answered by mananth)

The larger of two numbers is 8 more than twice the smaller. The sum of the numbers is 10... (answered by josgarithmetic)