SOLUTION: Sarah is eight more than four times as old as Denise. In 24 years the sum of their ages will be 116. How old is Denise now? OPTIONS ARE: 12 56 60 13

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Sarah is eight more than four times as old as Denise. In 24 years the sum of their ages will be 116. How old is Denise now? OPTIONS ARE: 12 56 60 13      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1001982: Sarah is eight more than four times as old as Denise. In 24 years the sum of their ages will be 116. How old is Denise now?
OPTIONS ARE:
12
56
60
13
Found 2 solutions by MathLover1, macston:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Sarah is eight more than four times as old as Denise.
Sarah=4%2ADenise%2B8...........eq.1
if in 24 years the sum of their ages will be 116, we have
%28Sarah%2B24%29%2B%28Denise%2B24%29=116
Sarah%2BDenise%2B48=116
Sarah%2BDenise=116-48
Sarah%2BDenise=68
Sarah=68-Denise....eq.2
since left sides of eq.1 and eq.2 are same, equal the right sides

4%2ADenise%2B8=68-Denise
4%2ADenise%2BDenise=68-8
5Denise=60
Denise=60%2F5
Denise=12
Denise is highlight%2812%29 years old now.
and Sarah=4%2ADenise%2B8=4%2A12%2B8=56
check:
in 24 years from now, Denise will be 12%2B24=36
in 24 years from now, Sarah will be 56%2B24=80
the sum will be 36%2B80=116

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
S=Sarah's current age; D=Denise's current age
.
(S+24)+(D+24)=116
S+D+48=116
S+D=68
S=68-D
.
S=4D+8
68-D=4D+8
60=5D
12=D
ANSWER: Denise is 12 years old.
.
CHECK:
S=68-D=68-12=56
Sarah is 56 years old.
.
S=4D+8
56=4(12)+8
56=48+8
56=56