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. number of teaspoons of herb per blend basil oregano parsley blend 1 1 2 3 blend 2 1 1 2 blend 3 2 2 1 cost blend 1 $1.06 blend 2 $0.72 blend 3 $0.99 what 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.
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 $x=0.38 - z$. Blend 3: $2x+2(0.34 - z)+z=0.99$, substitute $x = 0.38 - z$ into it: $2(0.38 - z)+2(0.34 - z)+z=0.99$. Expand: $0.76-2z + 0.68-2z+z=0.99$. Combine like - terms: $0.76 + 0.68-(2z + 2z - z)=0.99$. $1.44 - 3z=0.99$. $3z=1.44 - 0.99 = 0.45$. $z = 0.15$.
Step4: Find the value of $x$.
Since $x=0.38 - z$ and $z = 0.15$, then $x=0.38-0.15 = 0.23$.
Answer:
$0.23$