High School

Yoko's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Yoko $4.40 per pound, and Type B coffee costs $5.80 per pound. This month, Yoko made 157 pounds of the blend, for a total cost of $793.00. How many pounds of Type A coffee did she use?

Answer :

Yoko used 53 pounds of type A coffee.

To solve this problem, we can set up a system of equations based on the given information. Let (x) be the number of pounds of type A coffee and (y) be the number of pounds of type B coffee. The cost equation for type A coffee is (4.40x) and for type B coffee is (5.80y). Since Yoko made 157 pounds of the blend, we have the equation (x + y = 157).

The total cost equation is (4.40x + 5.80y = 793.00).

We can solve the system of equations to find the values of (x) and (y). By substituting (x = 157 - y) into the total cost equation, we get (4.40(157 - y) + 5.80y = 793.00). Simplifying this equation leads to (y = 53). Substituting (y = 53) into (x + y = 157) gives us (x = 157 - 53 = 104).

Therefore, Yoko used 53 pounds of type A coffee in her blend.

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