SOLUTION: Alice, Brent and Celeste are cousins. The sum of their ages is 76. The sum of the ages of alice and Celeste is 1 year more than Brent's age. Celeste is 7 1/2 years older than Alice

Question 946975: Alice, Brent and Celeste are cousins. The sum of their ages is 76. The sum of the ages of alice and Celeste is 1 year more than Brent's age. Celeste is 7 1/2 years older than Alice. What are the ages of Alice, Brent and Celeste?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Alice, Brent and Celeste are cousins.
call them a, b, & c; write an equation for each statement
:
The sum of their ages is 76.
a + b + c = 76
:
The sum of the ages of Alice and Celeste is 1 year more than Brent's age.
a + c = b + 1
or
a - b + c = 1
:
Celeste is 7 1/2 years older than Alice.
c = a + 7.5
:
take the 1st and 2nd equation,
a + b + c = 76
a - b + c = 1
---------------- adding eliminates b
2a + 2c = 77
substitute (a+7.5) for c, from the 3rd statement
2a + 2(a+7.5) = 77
2a + 2a + 15 = 77
4a = 77 - 15
4a = 62
a = 62/4
a = 15.5 yrs is Alice
then
c = 15.5 + 7.5
c = 23 yrs is Celeste
Find b using the first equation, replace a & c
15.5 + b + 23 = 76
b + 38.5 = 76
b = 76 -38.5
b = 37.5 yr is Brent
:
" What are the ages of Alice, Brent and Celeste? 15.5, 37.5, 23
:
See that they add up to 76
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