SOLUTION: Jose, Pedro, and Felipe are brothers and Pedro is the youngest. Felipe is 2 years older than Pedro, and Jose is 3 years older than Felipe. Three times the sum of Pedro and Felipe

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Jose, Pedro, and Felipe are brothers and Pedro is the youngest. Felipe is 2 years older than Pedro, and Jose is 3 years older than Felipe. Three times the sum of Pedro and Felipe      Log On


   

Question 246127: Jose, Pedro, and Felipe are brothers and Pedro is the youngest. Felipe is 2 years older than Pedro, and Jose is 3 years older than Felipe. Three times the sum of Pedro and Felipe’s age equals two less than the product of four and Jose’s age. Find the age of all the brothers.
Found 2 solutions by stanbon, marcsam823:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Jose, Pedro, and Felipe are brothers and Pedro is the youngest.
Felipe is 2 years older than Pedro, and Jose is 3 years older than Felipe. Three times the sum of Pedro and Felipe’s age equals two less than the product of four and Jose’s age. Find the age of all the brothers.
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Equations:
f = p+2
j = f+3
3(p+f)=4j-2
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Rearrange:
p = f-2
j = f+3
3f + 3p - 4j = -2
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Substitute:
3f + 3(f-2) -4(f+3) = -2
2f -14 = -2
2f = 12
f = 6 yrs (Felipe's age now)
p = f-2 = 4 yrs (Pedro's age now)
j = f+3 = 15 yrs (Jose's age now)

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Cheers,
Stan H.

Answer by marcsam823(57) About Me  (Show Source):
You can put this solution on YOUR website!
Define your terms:

Let x = Pedro's age
Let x + 2 = Felipe's age
Let x + 5 = Jose's age

Translate the words into an algebraic expression:

Three times the sum of Pedro and Felipe’s age = two less than the product of four and Jose’s age.

3(x + (x + 2)) = 4(x + 5) - 2

Solve for x:

3(2x + 2) = 4x + 20 - 2
6x + 6 = 4x +18
2x = 12

x = 6 = Pedro's age
x + 2 = 8 = Felipe's age
x + 5 = 11 = Jose's age