Question

How many per pounds of each kind should he use in the new mix round off the answer to nearest hundredth

Answer 1

14 pounds of $1.45 and 7 pounds of $2.20

STEP BY STEP EXPLANATION

Step 1:

let x be $1.45 per pound of coffee and

y be $2.20 per pound of coffee

He wants to mix a total of 21

The algebraic equation now is:

`\begin{gathered} x\text{ + y = 21}\ldots\ldots\ldots\ldots..\ldots..\ldots\ldots..(1) \\ x\text{ = 21 - y }\ldots\ldots\ldots\ldots\ldots\ldots\ldots.\ldots.(2) \end{gathered}`

Now, at the price of $1.70 per pound he will make $1.70 * 21 = $35.7

Step 2: Solve for y

`\begin{gathered} 1.45\text{ x + 2.20 y = 35.7} \\ 1.45\text{ (21 - y) + 2.20 y = 35.7} \\ 30.45\text{ - 1.45y + 2.20y = 35.7} \\ 0.75\text{ y = 5.25} \\ y\text{ = }(5.25)/(0.75)\text{ = 7} \end{gathered}`

Step 3: Solve for x

`\begin{gathered} \text{from equation 2} \\ x\text{ = 21- 7} \\ x\text{ = 14} \end{gathered}`

Hence, the grocer needs to use about 14 pounds of $1.45 and 7 pounds of $2.20 in the new mix.