# SOLUTION: A number equals the sum of two other numbers. The largest number diminished by 2 equals three times the smallest. The largest increased by 2 equals twice the result of diminishing

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 Click here to see ALL problems on Linear Equations And Systems Word Problems Question 171633: A number equals the sum of two other numbers. The largest number diminished by 2 equals three times the smallest. The largest increased by 2 equals twice the result of diminishing the middle number by 2. Find the numbers.Answer by ankor@dixie-net.com(15667)   (Show Source): You can put this solution on YOUR website!Three numbers a,b,c. a the largest, c the smallest : Write an equation for each statement arrange each in the standard form: : "A number equals the sum of two other numbers." a = b + c a - b - c = 0 ; "The largest number diminished by 2 equals three times the smallest." a - 2 = 3c a - 3c = 2 : " The largest increased by 2 equals twice the result of diminishing the middle number by 2." a + 2 = 2(b-2) a + 2 = 2b - 4 a - 2b = -4 -2 a - 2b = -6 : Arrange all three equations and add a - b - c = 0 a +0b -3c = 2 a -2b +0c = -6 ----------------- 3a - 3b - 4c = -4 ; From the 1st statement we know a = (b+c), substitute in the above equation 3(b+c) - 3b - 4c = -4 3b + 3c - 3b - 4c = -4 3b - 3b + 3c - 4c = -4 -c = -4 c = + 4 : Find a, from the 2nd statement a - 2 = 3c, substitute 4 for c a - 2 = 3(4) a = 12 + 2 a = 14 : Use the 1st statement to find b 14 = b + 4 b = 10 : : You can check these solutions in each statement