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?

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.

RELATED QUESTIONS
Sally is 8 years older than john. John is 14 years older than Karen. If the sum of their... (answered by ikleyn,josmiceli)

John is 2 years older than bill . If the sum of their ages is 36 , how old is john... (answered by ikleyn)

John is 5 years older than Yaw,if the sum of their ages is 19.How old is John (answered by Shin123,ikleyn)

Mary is 24 years older than her son John. The sum of their ages is 40. How old is John? (answered by rfer,Alan3354)

Leslie is eight years older than John, if the sum of their ages is 42, find their ages. (answered by Alan3354,josgarithmetic)

The sum of ages of john and mark is 29 years.john is 3 years older than mark.how old is... (answered by macston)

frances is 10 years older than john, and the sum of their ages is 54. How old is... (answered by vleith,stanbon)

Given that John is two years older than eric and the sum of whir ages is 26 years how old (answered by ikleyn)

lesie is 4 years older than john. the sum of their ages is 32. How old is Leslie? How old (answered by praseenakos@yahoo.com)