SOLUTION: The ratio of two numbers is 8 to 5. The difference of the numbers is 24. What are the numbers?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of two numbers is 8 to 5. The difference of the numbers is 24. What are the numbers?      Log On


   

Question 818855: The ratio of two numbers is 8 to 5. The difference of the numbers is 24. What are the numbers?
Answer by jhunjiro(67) About Me  (Show Source):
You can put this solution on YOUR website!
ratio +x%2Fy=8%2F5+ eq. 1
+x-y=24 eq.2
Manipulate eq. 1
+x%2Fy=8%2F5+
+cross+%28y%29%28x%2Fcross+%28y%29%29=%288%2F5%29y+
+x=8y%2F5+ eq. 3
Substitute eq. 3 to eq 2
+%288y%2F5%29-y=24+
+5%2A%28%288y%2F5%29-y%29=%2824%29%2A5++
+8y-5y=120++
+3y=120++
+3y%2F3=120%2F3+
+y=40++
+x=8%2840%29%2F5++
+x=320%2F5++
+x=64+
Final Answer:
The numbers are +highlight+%2864%29+ and +highlight+%2840%29+