Question 1168287
<br>
That other tutor really loves that general formula with all those different variables....<br>
I'm more in favor of a student UNDERSTANDING how to solve a problem, rather than plugging numbers into a mysterious formula.<br>
Algebraically, x pounds at $2.50 per pound, plus (480-x) pounds at $2.80 per pound, makes 180 pounds at $2.68 per pound:<br>
{{{x(2.50)+(480-x)(2.80) = 480(2.68)}}}<br>
Solve using basic algebra; although the calculations are a bit messy.<br>
Here is a quick and easy path to the solution to any 2-part mixture problem like this, if a formal algebraic solution is not required.<br>
Picture the three prices on a number line: 2.50, 2.68, and 2.80.
Determine with simple arithmetic that 2.68 is 18/30 = 3/5 of the way from 2.50 to 2.80.
That means 3/5 of the mixture is the higher priced coffee.<br>
ANSWER: 3/5 of the 480 pounds, or 288 pounds, of the $2.80 coffee; the other 192 pounds of the $2.50 coffee.<br>
CHECK:
288(2.80)+192(2.50) = 806.4+480 = 1286.4
480(2.68) = 1286.4<br>