SOLUTION: The larger of two numbers is 10 less than twice the smaller. If half the larger is increased by 4 times the smaller, the result is 50. Please help .

Question 554919: The larger of two numbers is 10 less than twice the smaller. If half the larger is increased by 4 times the smaller, the result is 50. Please help .
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The larger of two numbers is 10 less than twice the smaller. If half the larger is increased by 4 times the smaller, the result is 50.
:
Let x = the large number
let y = the smaller
:
Write an equation for each statement:
:
"The larger of two numbers is 10 less than twice the smaller."
x = 2y - 10
:
"If half the larger is increased by 4 times the smaller, the result is 50."
.5x + 4y = 50
From the 1st statement; replace x with (2y-10)
.5(2y - 10) + 4y = 50
y - 5 + 4y = 50
5y = 50 + 5
5y = 55
y = 55/5
y = 11
find x
x = 2y - 10
x = 2(11) - 10
x = 22 - 10
x = 12
:
:
Check our solution in the 2nd statement:
" If half the larger is increased by 4 times the smaller, the result is 50."
.5(12) + 4(11) =
6 + 44 = 50, confirms our solutions of x=12, y=11
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