word problem

Question

a store mixes kentucky blue grass worth $11 per pound and ryegrass worth $14 per pound. the mixture is to sell for $13 per pound. How much of each should be used to make a 204 pound mixture?

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is that you want to use the underlying information given in order to set up an equation that we can solve! On this one that means

x + y = 204   since there are 204 pounds total between the two types

11x + 14y = 13(204)    since the total cost after each type is accounted for should be $13/pound

From there then you just want to solve the expression algebraically! I think the best way is to plug in y = 204 – x into the second equation and then go from there! When I do that I get

x = 68 and y = 136 for the underlying values

meaning that the store should use 68 pounds of Kentucky blue grass and 136 pounds of ryegrass

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

let x=# of pounds of bluegrass

let 204-x=# of pounds of ryegrass

11(x)+14(204-x)=13(204)

11x+2856-14x=2652

-3x+2856=2652

-3x=2652-2856

-3x=-204

x=68 pounds of bluegrass

204-68=136 pounds of ryegrass

check:11(68)+14(136)=748+1904=$2652

13(204)=$2652