The sum of Buddy and Sol's age is 31. Ten years ago Sol's age was twice that of Buddy. Calculate their ages?

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Answer 1 · 2018-01-24T01:53:41

Buddy is 17 years old. Sol is 24 years old.

Equations
#B+S = 41#
#2(B-10)=S-10#

Solution
#S=2(B-10)+10#
#S=2B-10#
#B+2B-10=41#
#3B=51#
#B=17#
#S+17=41#
#S=24#

Answer 2 · 2018-01-24T01:58:38

Buddy is #17# and Sol is #24 #

If we denote Buddy's current age by #B#, ans Sol's age by #S# then:

The first line tells us that:

# B+S=41 #

Ten years ago, Buddy's age would have been #B-10# and Sol's age would have been #S-10#, so the second line tells us that:

# (S-10) = 2(B-10) #
# :. S-10 = 2B-20 #
# :. 2B-S = 10 #

We now need to solve the two equations simultaneously. If we add the two equations:

# 3B = 51 => B=17 #

And substituting this into the first equation:

# 17+S=41 => S=24 #

Hence:

# B=17 # and # S=24 #

Validation

# B + S = 17+24 = 41 #
# B-10 = 7# and #S-10=14#

Which satisfies the given conditions