Question

Omar's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Omar $4.05 per pound, and type B coffee costs $5.65 per pound. This month, Omar made 131 pounds of the blend, for a total cost of $626.55. How many pounds of type B coffee did he use?

Answer 1

b = 59.375

Explanation:

Let's call the number of pounds of type A coffee used in the blend "a" and the number of pounds of type B coffee used "b". We can set up a system of two equations to represent the information given:

a + b = 131 (the total amount of coffee used in the blend is 131 pounds)

4.05a + 5.65b = 626.55 (the total cost of the blend is $626.55)

We can solve for one of the variables in terms of the other using the first equation:

a = 131 - b

Substituting this into the second equation, we get:

4.05(131 - b) + 5.65b = 626.55

Distributing the 4.05, we get:

531.55 - 4.05b + 5.65b = 626.55

Combining like terms, we get:

1.6b = 95

Dividing both sides by 1.6, we get:

b = 59.375

So, 59.375 pounds of type B coffee.

Answer 2

60 pounds

`\hrulefill`

Explanation:

To calculate how many pounds of type B coffee Omar used to make his coffee blend, we can set up and solve a system of equations.

Let "A" be the number of pounds of type A coffee Omar used.

Let "B" be the number of pounds of type B coffee Omar used.

Given Omar made a total of 131 pounds of coffee blend:

`A+B=131`

Given type A coffee costs $4.05 per pound, and type B coffee costs $5.65 per pound, and the total cost for the blend was $626.55:

`4.05A+5.65B=626.55`

Therefore, the system of equations that models the given scenario is:

`\begin{cases}A+B=131\\4.05A+5.65B=626.55\end{cases}`

Rearrange the first equation to isolate A:

`\begin{aligned}A+B&=131\\A+B-B&=131-B\\A&=131-B\end{aligned}`

Substitute the expression for A into the second equation and solve for B:

`\begin{aligned}4.05(131-B)+5.65B&=626.55\\\\530.55-4.05B+5.65B&=626.55\\\\530.55+1.6B&=626.55\\\\530.55+1.6B-530.55&=626.55-530.55\\\\1.6B&=96\\\\(1.6B)/(1.6)&=(96)/(1.6)\\\\B&=60\end{aligned}`

Therefore, Omar used 60 pounds of type B coffee in his blend.