Question 1155346
<br>
Using a traditional algebraic approach....<br>
x pounds at $10.10 per pound, plus (20-x) pounds at $14.30 per pound equals 20 pounds at $13.46 per pound:<br>
{{{10.10(x)+14.30(20-x) = 13.46(20)}}}
{{{10.10x+286-14.30x = 269.2}}}
...<br>
You can finish the problem by that method....<br>
Here is a method for solving this problem by a very different method which requires less time and effort.<br>
Key idea: the ratio in which the two ingredients must be mixed is exactly determined by where the price of the mixture lies between the prices of the two ingredients.<br>
(1) 14.30-10.10 = 4.20
(2) 13.46-10.10 = 3.36
(3) The mixture price of $13.46 per pound is 336/420 = 84/105 = 4/5 of the way from the $10.10 price of the first ingredient and the $14.30 price of the second.
(4) That means 4/5 of the mixture needs to be the second ingredient.<br>
ANSWER: 4/5 of 20 pounds, or 16 pounds, of the Arabian Mocha blend; the remaining 4 pounds of the Mexican blend.<br>
CHECK:
16(14.30)+4(10.10) = 269.2
20(13.46) = 269.2<br>