Mixture Problem 3 Solution

This mixture problem deals with dollars instead of percentages. But, works the same way as before.

She has 10 pounds of $3 coffee for a total worth of $30 and x pounds of $5 coffee. The question asks of how much of the x $5 coffee is needed to mix with the 10 pounds of $3 coffee to make (10 + x) pounds of $4.50 coffee with a total value of $4.50 * (10 + x)

to set this up we would then have:

3(10) + 5x = (10 + x) * 4.50

30 + 5x = 45 + 4.50 x *multiply by 100 to get rid of decimal

3000 + 500x = 4500 + 450x

50x = 1500

x = 1500/50

x = 30

so 30 pounds of the $5 grade must be added to the 10 pounds of $3 grade to make $4.50 grade-- If you think about it that makes sense. If you had exactly the same amount of $5 coffee (10 pounds) as the $3 coffee-- then that would make an average grade of $4 coffee--- so you know it would have to be a lot more than just 10 pounds to increase the value close to $5-- which 30 pounds does.

But, just to check..

Does

30 + 5(30) = (10 + 30) * 4.50 ?

30 + 150 = 40(4.50)

180 = 180 correct