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

Question 116921: twice the larger of two numbers is three more than five times the smaller and the sum of four times the larger and three times the smaller is 71.What are the numbers?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
twice the larger of two numbers is three more than five times the smaller
EQUATION:
Let "x" be the larger and "y" the smaller number:
2x = 5y+3
---------------
the sum of four times the larger and three times the smaller is 71.What are the numbers?
EQUATION:
5x+3y = 71
-----------------
Rearrange:
2x-5y = 3
5x+3y = 71
-----------------
Multiply 1st equation by 5 and 2nd equation by 2 to get:
10x-25y = 15
10x+6y = 142
-----------------
Subtract 1st from 2nd to solve for "y:
31y = 127
y = 127/31 =4.09
--------------------
Substitute into 2x-5y = 3 to solve for "x"
2x-5(127/31) = 3
2x-635/31 = 3
2x = 728/31
x = 364/31 =11.74
------------------
Cheers,
Stan H.
RELATED QUESTIONS
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 the two numbers is three more than five times the smaller, and then... (answered by ankor@dixie-net.com)

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 sum of two numbers is 23. the difference between three times the smaller and seven is (answered by nerdybill)

find two numbers such that five times the larger plus three times the smaller is 47 and... (answered by Mathtut)

find two numbers such that five times the larger plus three times the smaller is 47,and... (answered by orca)