Mixture...2

A store owner wants to mix cashews and almonds. Cashews cost 2 dollars per pound and almonds cost 5 dollars per pound. He plans to sell 150 pounds of a mixture. How many pounds of each type of nuts should be mixed if the mixture will cost 3 dollars?

I can set up two equations in two unknowns but there is a "mixture way" to solve this problem involving only one variable.

Let p = pounds

2p = cashews

5p = almonds

Stuck....

 

Let x be the number of pounds of cashews.

So, 150 - x will represent the number of almonds.

Since each pound of the mixture costs 3 dollars, 150 pounds will cost 3 × 150 = 450 dollars.

Cost of cashews + cost of almonds = 450

2 × x + (150 - x) × 5 = 450

2x + 150 × 5 - x × 5 = 450

2x + 750 - 5x = 450

2x - 5x + 750 = 450

-3x + 750 = 450

-3x + 750 - 750 = 450 - 750

-3x = -300

-3x/-3 = -300/-3

x = 100

150 - x = 150 - 100 = 50.

The store owner should mix 100 pounds of cashews with 50 pounds of almonds.

 

I think the time has come for me to realize that it is not possible to understand every math topic. Word problems will forever be foreign to me.