Problema Solution
The sum of three numbers is 48. The sum of the two larger numbers is three times the smallest. The sum of the two smaller numbers is 6 more than the largest. Find the Numbers.----You must set up a system of algebraic equations and solve it.
Answer provided by our tutors
let the numbers be represented by 'a', 'b' and 'c' such as a < b < c
b+c = 3a
a+b = c+6
a+b+c = 48
we subtract the last two equations:
a+b = c+6
a+b+c = 48
to get:
2c = 48-6
c=42/2 = 21
the larger number is 21
now we subtract the first two equations with 'c' replaced by '21'
b+21 = 3a
a+b = 21+6
to get:
a-21 = 27-3a
4a = 48
a = 48/4 = 12
the smallest number is 12
finally, we use the first equation to solve for 'b':
12 + b + 21 = 48
b = 48 - 12 - 21 = 15
the numbers are 12, 15 and 21