SOLUTION: Michael's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Michael $4.60 per pound, and type B coffee costs $5.95 per pound. This month's ble

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Michael's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Michael $4.60 per pound, and type B coffee costs $5.95 per pound. This month's ble      Log On


   

Question 894024: Michael's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Michael $4.60 per pound, and type B coffee costs $5.95 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $830.65. How many pounds of type A coffee were used?
I see that there are a lot of similar problems like this but none that help me with the given variables. :p
Please help. :)
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
This looks very familiar.
Let u = how many pounds type A
Let v = how many pounds type B

Note that the description gives how u and v are related.
That description gives v%2Fu=3 which means v=3u.

Account for the cost of the blend using the prices given in the description.
4.60u%2B5.95v=830.65

The question asks for how much of type A, which corresponds to the variable, u.
Substituting for v will give you a cost equation in just the one variable you are asked to find, which is u:
highlight_green%284.60u%2B5.95%283%2Au%29=830.65%29;
Now just solve for u.

This cannot be any simpler.