SOLUTION: A silversmith wishes to obtain an alloy containing at least 72% silver and at most 75% silver. Determine the greatest and least amounts of an 80% silver alloy that should be combin

Question 995434: A silversmith wishes to obtain an alloy containing at least 72% silver and at most 75% silver. Determine the greatest and least amounts of an 80% silver alloy that should be combined with a 65% silver alloy in order to have 30grams of the required alloy.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
This is 2 problems in 1
Let = grams of 80% alloy needed
Let = grams of 65% alloy needed
---------------------------------
First solve for 72% silver end result
(1)
(2)
-----------------------------
(2)
(2)
(2)
(2)
-----------------------
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
-----------------------

and
(1)
(1)
-----------------------
-----------------------
Now solve for 75% alloy end result
(1)
(2)
-----------------------------
(2)
(2)
(2)
(2)
------------------------
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
------------------------

and
(1)
(1)
------------------
From these results,
the least amount of 80% alloy needed is 14 grams ( making 72% silver )
the most amount of 80% alloy needed is 20 grams ( making 75% silver )
-------------------
You can check the answers by plugging
and back into (2) for both
72% and 75% cases
RELATED QUESTIONS
A silversmith has two alloys, one containing 70% silver and the other 40% silver. How... (answered by Maths68)

A silversmith has two alloys, one containing 35% silver and the other 66% silver. How... (answered by Fombitz)

A silversmith has two alloys, one containing 60% silver and the other 20% silver. How... (answered by nyc_function)

A silversmith has two alloys, one containing 70% silver and the other 30% silver. How... (answered by stanbon)

A silversmith has two alloys, one containing 70% silver and the other 20% silver. How... (answered by KMST)

A silversmith has two alloys, one containing 60% silver and the other 40% silver. How... (answered by mananth)

A silversmith has two alloys, one containing 60% silver and the other 40% silver. How... (answered by Alan3354)

A silversmith has two alloys, one containing 50% silver and the other 30% silver. How... (answered by josgarithmetic)

A silversmith has two alloys, one containing 50% silver and the other 40% silver. How... (answered by ikleyn)