Shin's coffee shop mixes a brand that is a mixture of two types of coffee: type A costs $4.05 per pound, and type B costs $5.25 per pound. This month, Shin made 157 pounds of the blend for a total cost of $752.25. How many pounds of type B did he use?

To find out how many pounds of type B coffee were used in the blend, we need to set up an equation using the cost and weight information. By simplifying and solving the equation for x, we find that 32 pounds of type B coffee were used.

Explanation:

In this problem, we have a blend of two types of coffee - type A costing $4.05 per pound and type B costing $52.50 per pound. The shop made 157 pounds of the blend costing $752.25 in total. We need to find how many pounds of type B coffee were used.

Let's assume the number of pounds of type A coffee used is x. Then the number of pounds of type B coffee used is 157 - x (since the total blend is 157 pounds).
The cost of the type A coffee used is 4.05x (since the cost per pound is $4.05).
The cost of the type B coffee used is 52.50(157 - x) (since the cost per pound is $52.50).
We can now form an equation: 4.05x + 52.50(157 - x) = 752.25 to solve for x.
By simplifying and solving the equation, we find that x = 125. Therefore, 125 pounds of type A coffee and 32 pounds of type B coffee were used in the blend.

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Final answer:

The question is about Mathematics, specifically system of equations. We created two equations using the given data. We then demonstrated how to solve these equations using substitution method to find the amount of type B coffee used in the blend.

Explanation:

Based on the information provided, we know that the cost of all the coffee is $752.25, and the total weight of the coffee blend is 157 pounds. We can create a system of equations to solve for the amount of each coffee type used in the blend. Let's say that A is the amount of type A coffee and B is the amount of type B coffee. Then, the equations would be: 4.05A + 52.5B = 752.25 and A + B = 157. We can solve this using the Elimination or Substitution method.

Using the Substitution method, we can express A as 157 - B from the second equation, and then substitute this into the first equation. This leads to: 4.05(157 - B) + 52.5B = 752.25. Solving this equation will provide the value of B - the amount of type B coffee used in the blend.

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