a company sells herb blends for cooking. the tables below show the number of teaspoons of each herb in each…

a company sells herb blends for cooking. the tables below show the number of teaspoons of each herb in each blend and the cost for each blend.\n\nnumber of teaspoons of herb per blend\n| | basil | oregano | parsley |\n|--|--|--|--|\n| blend 1 | 1 | 2 | 3 |\n| blend 2 | 1 | 1 | 2 |\n| blend 3 | 2 | 2 | 1 |\n\ncost\n| | |\n|--|--|\n| blend 1 | $1.06 |\n| blend 2 | $0.72 |\n| blend 3 | $0.99 |\n\nwhat is the cost of basil per teaspoon?

a company sells herb blends for cooking. the tables below show the number of teaspoons of each herb in each blend and the cost for each blend.\n\nnumber of teaspoons of herb per blend\n| | basil | oregano | parsley |\n|--|--|--|--|\n| blend 1 | 1 | 2 | 3 |\n| blend 2 | 1 | 1 | 2 |\n| blend 3 | 2 | 2 | 1 |\n\ncost\n| | |\n|--|--|\n| blend 1 | $1.06 |\n| blend 2 | $0.72 |\n| blend 3 | $0.99 |\n\nwhat is the cost of basil per teaspoon?

Answer

Explanation:

Step1: Let the cost per - teaspoon of basil be $x$, oregano be $y$, and parsley be $z$.

Based on Blend 1: $x + 2y+3z=1.06$; Based on Blend 2: $x + y + 2z=0.72$; Based on Blend 3: $2x+2y + z=0.99$.

Step2: Subtract the equation of Blend 2 from the equation of Blend 1.

$(x + 2y+3z)-(x + y + 2z)=1.06 - 0.72$ $x + 2y+3z-x - y - 2z=0.34$ $y + z=0.34$, so $y=0.34 - z$.

Step3: Substitute $y = 0.34 - z$ into the equations of Blend 1 and Blend 3.

For Blend 1: $x+2(0.34 - z)+3z=1.06$, which simplifies to $x + 0.68-2z+3z=1.06$, then $x+z=1.06 - 0.68=0.38$, so $x=0.38 - z$. For Blend 3: $2x+2(0.34 - z)+z=0.99$. Substitute $x = 0.38 - z$ into $2x+2(0.34 - z)+z=0.99$: $2(0.38 - z)+2(0.34 - z)+z=0.99$. $0.76-2z + 0.68-2z+z=0.99$. $1.44-3z=0.99$. $3z=1.44 - 0.99=0.45$. $z = 0.15$.

Step4: Find the value of $x$.

Since $x=0.38 - z$ and $z = 0.15$, then $x=0.38-0.15 = 0.23$.

Answer:

$0.23$