Question 1186116
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The solution from the other tutor is fine.  But nearly always an algebraic solution is easier if you set up the problem using a single variable.<br>
x = pounds of Indonesian cinnamon at $19/lb
16-x = pounds of Thai cinnamon at $11/lb<br>
The 16 pounds mixture costs $17/lb:<br>
{{{19(x)+11(16-x)=17(16)}}}
{{{19x+176-11x=272}}}
{{{8x=96}}}
{{{x=12}}}<br>
ANSWER:
Indonesian cinnamon: x=12 pounds
Thai cinnamon: 16-x=4 pounds<br>
CHECK: 19(12)+11(4)=228+44=272<br><hr>
Presumably this problem is to be solved by a student who is just learning how to use algebra to solve problems, so a formal algebraic solution like the one above is what was wanted.<br>
However, if a formal algebraic solution is not required, the answer to any 2-part mixture problem like this can be found quickly with a bit of easy mental arithmetic.<br>
(1) Observe/calculate that the $17 per pound cost of the mixture is 3/4 of the way from the $11 per pound cost of the Thai cinnamon to the $19 per pound cost of the Indonesian cinnamon.
(2) That means 3/4 of the mixture is the more expensive cinnamon.<br>
ANSWER: 3/4 of 16 pounds, or 12 pounds, of Indonesian cinnamon, the other 4 pounds of Thai cinnamon.<br>