# 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 .

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 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(15746)   (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