Problema Solution
bianca, nina and angelica are classmates in thier algebra class. their instructor wants to know their individual ages by means of clues. they told their instructor the first clue that the sum of their ages is eleven more than twice bianca's age. secondly if they deduct angelica's age from bianca's age it will be one more than quarter of the age of nina. lastly if they combine bianca's and nina's ages in two years, it will be ten more than twice that of angelica's present age. what are their present ages?
Answer provided by our tutors
let 'b' represent Bianca's age, 'a' represent Angelica's age and 'n' represent Nina's age
sum of their ages is eleven more than twice bianca's age:
a+b+n = 2b + 11
if they deduct angelica's age from bianca's age it will be one more than quarter of the age of nina:
(b-a) = (n/4) + 1
if they combine bianca's and nina's ages in two years, it will be ten more than twice that of angelica's present age:
(b+2) + (n+2) = 2a+10
so we have these equations:
a+b+n = 2b + 11
(b-a) = (n/4) + 1
(b+2) + (n+2) = 2a+10
solving this system of equations, we have:
a = 15
b = 20
n = 16
Bianca is 20, Nina is 16 and Angelica is 15