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

Algebra ->  Test -> 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      Log On


   



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) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = Alvero's age now
Let b= Alyssa's age now
given:
(1) +%28+a+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F5+
(2) +%28+a+%2B+10+%29+%2F+%28+b+%2B+10+%29+=+2%2F3+
--------------------------
(1) +5%2A%28+a+%2B+5+%29+=+3%2A%28+b+%2B+5+%29+
(1) +5a+%2B+25+=+3b+%2B+15+
(1) +5a+-+3b+=+-10+
and
(2) +3%2A%28+a+%2B+10+%29+=+2%2A%28+b+%2B+10+%29+
(2) +3a+%2B+30+=+2b+%2B+20+
(2) +3a+-+2b+=+-10+
------------------
Multiply both sides of (1) by 2 and
multiply both sides of (2) by 3
Then subtract (2) from (1)
(1) +10a+-+6b+=+-20+
(2) +-9a+%2B+6b+=+30+
+a+=+10+
and
(1) +5a+-+3b+=+-10+
(1) +5%2A10+-+3b+=+-10+
(1) +-3b+=+-10+-+50+
(1) +b+=+20+
The sum of their ages is 30
check answer:
(1) +%28+a+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F5+
(1) +%28+10+%2B+5+%29+%2F+%28+20+%2B+5+%29+=+3%2F5+
(1) +15%2F25+=+3%2F5+
(1) +3%2F5+=+3%2F5+
OK
(2) +%28+a+%2B+10+%29+%2F+%28+b+%2B+10+%29+=+2%2F3+
(2) +%28+10+%2B+10+%29+%2F+%28+20+%2B+10+%29+=+2%2F3+
(2) +20%2F30+=+2%2F3+
(2) +2%2F3+=+2%2F3+
OK

Answer by Maths68(1474) About Me  (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