Question 720762: Alice, Brent, and Celeste are cousins. The sum of their age is 76. The sum of the ages of Alice and Celeste is one more year than Brent's age. Celeste is 7 1/2 years younger 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. The sum of their age is 76.
a + b + c = 76
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The sum of the ages of Alice and Celeste is one more year than Brent's age.
a + c = b + 1
a - b + c = 1
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Celeste is 7 1/2 years younger than Alice.
c = a - 7.5
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What are the ages of Alice, Brent, and Celeste?
:
Use elimination with the 1st and 2nd equations
a + b + c = 76
a - b + c = 1
---------------Subtraction eliminates a and c find b
0 +2b + 0 = 75
b = 75/2
b = 37.5 yrs
therefore
a + c = 76 - 37.5
a + c = 38.5
replace c with (a-7.5)
a + a - 7.5 = 38.5
2a = 38.5 + 7.5
2a = 46
a = 46/2
a = 23 yrs
then
c = 23 - 7.5
c = 15.5 yrs
:
:
see if that checks out
23 + 37.5 + 15.5 = 76
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