SOLUTION: one number is 10 more than the 1/3 of the second number find the numbers for which the product is a minimum then find the minimum product

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: one number is 10 more than the 1/3 of the second number find the numbers for which the product is a minimum then find the minimum product       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1025104: one number is 10 more than the 1/3 of the second number find the numbers for which the product is a minimum then find the minimum product
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be +x+ and +y+
+x+=+%281%2F3%29%2Ay+%2B+10+
The product is:
+x%2Ay+
+%281%2F3%29%2Ay+%2B+10+=+x+
+%281%2F3%29%2Ay+=+x+-+10+
+y+=+3x+-+30+
----------------
+x%2Ay+=+x%2A%28+3x+-+30+%29+
+x%2Ay+=+3x%5E2+-+30x+
--------------------
The formula for minimum is:
+x%5Bmin%5D+=+-b%2F%282a%29+
+x%5Bmin%5D+=+-%28-30%29+%2F+%28+2%2A3+%29+
+x%5Bmin%5D+=+5+
and
+y+=+3x+-+30+
+y+=+-15+
--------------------
When the numbers are 5 and -15, the product is a minimum
The minimum product is +5%2A%28-15%29+=+-75+
------------------
check:
Suppose +x+=+5.1+
+y+=+3x+-+30+
+y+=+15.3+-+30+
+y+=+-14.7+
+x%2Ay+=+5.1%2A14.7+
+x%2Ay+=+-74.97+
This is larger than +-75+, so
+5%2A%28-15%29+ seems to be the minimum