A mixture problem

A store mixes red fescue worth $10 per pound and ryegrass worth $13 per pound. The mixture is to sell for $12 per pound. Find how much of each should be used to make a 264 pound mixture.

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x = pounds of $10 per pound red fescue
264 - x = pounds of $13 per pound ryegrass   {the mixture is 264 total pounds}

10x + 13(264 - x) = 12(264)   {price multiplied by number of pounds equals total value}
10x + 3432 - 13x = 3168   {used distributive property and multiplied}
-3x + 3432 = 3168   {combined like terms}
-3x = -264   {subtracted 3432 from each side}
x = 88 pounds of $10/pound red fescue   {divided each side by -3}
264 - x = 176 pounds of $13 per pound ryegrass   {substituted 88, in for x, into 264 - x} 

88 pounds of $10 per pound red fescue
176 pounds of $13 per pound ryegrass


- Algebra House