A pet store owner wants to mix together an high quality dry cat food costing 1.10 per pound with a lower quality dry cat food costing 0.85 per pound. How many pounds of each should be mixed together in order to produce 40 pounds of a mixture costing 0.95 per pound?
I think I know how to start part of the problem but I am stuck on the second part of the problem. This is what I have gotten so far:
$$1.10x+0.85y= $$
Is this the right approach to this problem?
On
You are on the right track. Let x be the amount of expensive food and y the amount of cheap food. The equation you've already written is for the total cost, which we can extend to 1.10x+0.85y=40*0.95
You have two variables, so you need a second equation. The second equation I would use is x+y=40
Try working with the two equations, in two unknowns:
You can finish your first equation (sum of cost of more expensive food (x pounds at a cost of $1.10$) and the cost of the leass expensive food (y pounds at a cost of .85 per pound) by noting we want a total of $40$ pounds costing 0.95 per pound for a total cost of $.95\times 40$:
$$1.10x+0.85y= 0.95\times 40\tag{1}$$
The number of total pounds needed is the sum of the weights, in pounds, given by $x + y$: $$x + y = 40\tag{2}$$