SOLUTION: Sam is ten less than 3 times as old as Alex. If the difference between their ages is 28, How old is Sam and Alex?

Question 1122372: Sam is ten less than 3 times as old as Alex. If the difference between their ages is 28, How old is Sam and Alex?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let age of sam be equal to x.
let age of alex be equal to y.

age of sam is 10 less than 3 times the age of alex.

formula for that is x = 3 * y - 10

the difference between their ages is 28.

formula for that is x - y = 28

in this last formula, solve for x to get x = y + 28

in the first formula, replace x with y + 28 to get y + 28 = 3 * y - 10

subtract y from both sides of the equation and add 10 to both sides of the equation to get:

28 + 10 = 3 * y - y

combine like terms to get 38 = 2 * y

solve for y to get y = 38 / 2 = 19

since x = 3 * y - 10, then x must be equal to 47.

you have:

age of sam is 47
age of alex is 19

age of sam is 3 * age of alex minus 10.
that becomes 47 = 3 * 19 - 10 which becomes 47 = 47, confirming this part of the solution is correct.

the difference between their ages is 28.
47 - 19 = 28, confirming this part of the solution is correct.

solution looks good.

sam is 47 and alex is 19.

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