Equations and Inequalities
Solving a value mixture problem using a linear equation
Ryan
Deshaun's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Deshaun $\$ 4.55$ per pound, and type B coffee costs $\$ 5.70$ per pound. This month, Deshaun made 117 pounds of the blend, for a total cost of $\$ 589.85$. How many pounds of type B coffee did he use?
Number of pounds of type B coffee:
$x$
5

Step 1 ：Let's denote the weight of type A coffee as \(x\) and the weight of type B coffee as \(y\).

Step 2 ：We know that the total weight of the coffee blend is 117 pounds, so we can write the equation: \(x + y = 117\).

Step 3 ：We also know that the total cost of the blend is $589.85, and the cost per pound of each type of coffee. This gives us the equation: \(4.55x + 5.70y = 589.85\).

Step 4 ：We can solve these two equations to find the values of \(x\) and \(y\).

Step 5 ：The solution to the equations is \(x = 67\) and \(y = 50\).

Step 6 ：So, the number of pounds of type B coffee Deshaun used is \(\boxed{50}\).