SOLUTION: The ratio of the ages of Mandy and Sandy is 2:5. After 8 years, their ages will be in the ratio 1:2. What is the difference between their present ages? Caitlin says the differen

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The ratio of the ages of Mandy and Sandy is 2:5. After 8 years, their ages will be in the ratio 1:2. What is the difference between their present ages? Caitlin says the differen      Log On


   

Question 1029839: The ratio of the ages of Mandy and Sandy is 2:5. After 8 years, their ages will be in the ratio 1:2. What is the difference between their present ages?
Caitlin says the difference in their ages is 24 years. In two or more complete sentences, explain whether or not Caitlin is correct. In your explanation, include the equations and calculations necessary to support or contradict Caitlin's answer.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = Mandy's age now
Let +s+ = Sandy's age now
--------------------------
(1) +m%2Fs+=+2%2F5+
(2) +%28+m+%2B+8+%29+%2F+%28+s+%2B+8+%29+=+1%2F2+
-----------------------------
Multiply both sides of (2) by +2%2A%28+s+%2B+8+%29+
(2) +2%2A%28+m+%2B+8+%29+=+s+%2B+8+
(2) +2m+%2B+16+=+s+%2B+8+
(2) +s+-+2m+=+8+
and
(1) +5m+=+2s+
(1) +s+=+%285%2F2%29%2Am+
By substitution:
(2) +%285%2F2%29%2Am+-+2m+=+8+
(2) +5m+-+4m+=+16+
(2) +m+=+16+
and
(1) +s+=+%285%2F2%29%2Am+
(1) +s+=+%285%2F2%29%2A16+
(1) +s+=+40+
-----------------
+s+-+m+=+40+-+16+
+s+-+m+=+24+
-----------------
Yes the difference in their ages is 24
-----------------
check:
(2) +%28+m+%2B+8+%29+%2F+%28+s+%2B+8+%29+=+1%2F2+
(2) +%28+16+%2B+8+%29+%2F+%28+40+%2B+8+%29+=+1%2F2+
(2) +24%2F48+=+1%2F2+
(2) +1%2F2+=+1%2F2+
OK
(1) +m%2Fs+=+2%2F5+
(1) +16%2F40+=+2%2F5+
(2) +2%2F5+=+2%2F5+
OK