Question

Amanda's Coffee Shop makes a blend that is a mixture of two types of coffee. A coffee costs Amanda $5.60 per pound, and type B coffee costs $4.55 per pound. This month, Amanda made 141 pounds of the blend, for a total cost of $728.70. How many pounds of type B coffee did she use?

Answer 1

We are given that Amanda made 141 pounds of coffee. If "x" is the pounds of type A coffee and "y" is the amount of type b coffee then we can write this mathematically as:

`x+y=141,(1)`

We are also given that the cost of type A is $5.6 per pound and that the cost of type B is $4.55 per pound and that the total cost is $728.70, this can be written mathematically as:

`5.6x+4.55y=728.7,(2)`

Now, we solve for "x", first by subtracting "y" from both sides:

`y=141-x`

Now, we substitute the value of "y" in equation (2):

`5.6x+4.55(141-x)=728.7`

Now, we apply the distributive property in the parenthesis:

`5.6x+641.55-4.55x=728.7`

Now, we add like terms:

`1.05x+641.55=728.7`

Now, we subtract 641.55 from both sides:

`\begin{gathered} 1.05x=728.7-641.55 \\ 1.05x=87.15 \end{gathered}`

Now, we divide both sides by 1.05:

`x=(87.15)/(1.05)`

solving the operations:

`x=83`

Now, we substitute the value of "x" in equation (1):

`\begin{gathered} y=141-83 \\ y=58 \end{gathered}`

Therefore, the amount of coffee type A is 83 pounds and type B is 58 pounds.