SOLUTION: In 5 years the ratio of Alvaro�s age to Alyssa�s age will be 3:5. In ten years, the ratio of Alvaro�s age to Alyssa�s age will be 2:3. What is the sum of their current ages? Ans

Question 511352: In 5 years the ratio of Alvaro�s age to Alyssa�s age will be 3:5. In ten years, the ratio of Alvaro�s age to Alyssa�s age will be 2:3. What is the sum of their current ages?
Answer
a. 20
b. 30
c. 35
d. 40
e. 15
Found 2 solutions by josmiceli, Maths68:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = Alvero's age now
Let = Alyssa's age now
given:
(1)
(2)
--------------------------
(1)
(1)
(1)
and
(2)
(2)
(2)
------------------
Multiply both sides of (1) by and
multiply both sides of (2) by
Then subtract (2) from (1)
(1)
(2)

and
(1)
(1)
(1)
(1)
The sum of their ages is 30
check answer:
(1)
(1)
(1)
(1)
OK
(2)
(2)
(2)
(2)
OK
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Present age of Alvaro =a
Present age of Alyssa =s
============================================================================
In 5 years means we have add 5 in their present age
Alvaro�s age in five years = a+5
Alyssa�s age in five years = s+5
Then the ratio of Alvaro�s age to Alyssa�s age will be 3:5
(a+5):( s+5) = 3:5
a+5 / s+5 = 3/5
5(a+5)=3(s+5)
5a+25=3s+15
5a=3s+15-25
5a=3s-10
a=(3s-10)/5.................(1)
In ten years, the ratio of Alvaro�s age to Alyssa�s age will be 2:3. Same procedure will be applied for 10 years
(a+10):( s+10) = 2:3
a+10 / s+10 = 2/3
3(a+10)= 2(s+10)
3a+30=2s+20
3a=2s+20-30
3a=2s-10
a=(2s-10)/3��(2)
Put the value of a from (1) to (2)
(3s-10)/5=(2s-10)/3
(3)(3s-10)=(5)(2s-10)
9s-30=10s-50
9s-10s=10s-50+30
-s=-20
Multiply by (-1) both sides
s=20
Put the value s in (1)
a=(3s-10)/5��..(1)
a=(3(20)-10)/5
a=(60-10)/5
a=50/5
a=10
=============================================================================
Present age of Alvaro =a=10 years old
Present age of Alyssa =s = 20 years old
Sum of their ages = 20+10 = 30
==============================================================================
Check
(a+5):( s+5) = 3:5
(10+5):(20+5)=3:5
15:25=3:5
3:5=3:5
=======================================
(a+10):( s+10) = 2:3
(10+10):(20+10) = 2:3
20:30=2:3
2:3=2:3

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