Question 229586
let L = Larry's present age
Let B = Beth's present age
;
Write an equation for each statement:
:
"Larry is 15 Years older than Beth,"
L = B + 15
:
"In 4 Years Larry will be one year older than Twice Beth's age."
L + 4 = 2(B+4) + 1
Multiply what's inside the brackets, Simplify
L + 4 = 2B + 8 + 1
L + 4 = 2B + 9
Subtract 4 from both sides
L = 2B + 9 - 4
L = 2B + 5
:
 Find their ages today. 
Substitute (B+15) for L in the above equation
B + 15 = 2B + 5
Combine like terms
15 - 5 = 2B - B
10 = B
Beth is 10 yrs old
then
15 + 10 = 25 yrs is Larry's present age
:
:
Check these solution in the statement:
""In 4 Years Larry will be one year older than Twice Beth's age."
25 + 4 = 2(10+4) + 1
29 = 2(14) + 1; confirms our solution