# SOLUTION: Sally is eight years older than John. John is fourteen years older than Kareem. If the sum of all three ages is 90, how old is Kareem?

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 Click here to see ALL problems on Age Word Problems Question 303623: Sally is eight years older than John. John is fourteen years older than Kareem. If the sum of all three ages is 90, how old is Kareem?Answer by graphmatics(170)   (Show Source): You can put this solution on YOUR website!We can solve the system if we knew John's age,x, Sally's age ,y, and the solution Kareem's age, z. The first sentence say Sally is eight years older than John, so y = x+8 The second sentence say x = z+14 The last sentence says that the sum x+y+z is 90 so x+y+z = 90. The easy way to solve this 3 by 3 system of equations is simply to first rearrange the second equation to z = x-14. Now our 3x3 system is: y = x+8 z = x-14 x+y+z = 90 now put the first and second equation's expression for y and z respectively into the third equation and get the new third equation: x+(x+8)+(x-14) = 90 Solve the equation for John's age, x, and get: 3x = 90+14-8 3x = 96 x = 96/3 = 32 so using the second equation, z = x-14, to find Zareem's age, z, we get: z = 32-14 = 18 So Kareem's age, the value of z, is 18.