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.

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}

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 ryegrass176 pounds of $13 per pound ryegrass

*- Algebra House*