Question

how many pounds of chamomile tea that costs $18.10 per pound must be mixed with 16 lb of orange tea that costs $12.25 per pound to make a mixture that costs $14.20 per pound? 1.2 × lb. suggested tutorial: learn it solve a value - mixture application using a linear equation in one variable

Explanation:

Step1: Set up the equation

Let $x$ be the number of pounds of chamomile tea. The cost of the chamomile tea is $18.10x$, the cost of the orange - tea is $12.25\times16$, and the cost of the mixture is $14.20(x + 16)$. So the equation is $18.10x+12.25\times16=14.20(x + 16)$.

Step2: Expand and simplify the equation

First, calculate $12.25\times16 = 196$ and expand the right - hand side: $18.10x+196=14.20x+14.20\times16$. Then $18.10x+196=14.20x + 227.2$. Subtract $14.20x$ from both sides: $18.10x-14.20x+196=14.20x-14.20x + 227.2$, which gives $3.9x+196 = 227.2$.

Step3: Solve for $x$

Subtract 196 from both sides: $3.9x+196 - 196=227.2 - 196$, so $3.9x=31.2$. Divide both sides by 3.9: $x=\frac{31.2}{3.9}=8$.

Answer:

8