SOLUTION: Ben's age is four years less than three times that of his younger sister Amy. Half of Ben's age increased by Amy's age is 2 years more than twice Amy's age. Find their ages.

Question 167468: Ben's age is four years less than three times that of his younger sister Amy. Half of Ben's age increased by Amy's age is 2 years more than twice Amy's age. Find their ages.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let b = Ben's age now
Let a = Amy's age now
;
Write an equation for each statement:
:
"Ben's age is four years less than three times that of his younger sister Amy."
b = 3a - 4
:
" Half of Ben's age increased by Amy's age is 2 years more than twice Amy's age."
b + a = 2a + 2
subtract a from both sides
b = 2a - a + 2
b = a + 2
Multiply both sides by 2 to get rid of the fraction
b = 2(a+2)
b = 2a + 4
:
Find their ages.
;
Substitute (3a-4) for b in the above equation
3a - 4 = 2a + 4
:
3a - 2a = 4 + 4
:
a = 8 yrs is Amy's age
:
Find b
b = 2a +4
b = 2(8) + 4
b = 20 yrs is Ben's age
:
:
Check solution in the statement:
" Half of Ben's age increased by Amy's age is 2 years more than twice Amy's age."
20 + 8 = 2(8) + 2
10 + 8 = 16 + 2
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