https://file.aiquickdraw.com/mathbot/file/1730173155340pix6mivt.jpg

To solve this problem, let's set up a system of equations based on the given information.

Let:
- $ x $ = pounds of type A coffee.
- $ y $ = pounds of type B coffee.

### Given Information:
1. The total weight of the blend is 157 pounds:
   \[
   x + y = 157
   \]

2. The total cost of the blend is $753.90. Type A coffee costs $5.70 per pound, and type B coffee costs $4.20 per pound:
   \[
   5.7x + 4.2y = 753.90
   \]

### Solving the System of Equations

#### Step 1: Solve the first equation for $ x $ in terms of $ y $:
   \[
   x = 157 - y
   \]

#### Step 2: Substitute $ x = 157 - y $ into the second equation:
   \[
   5.7(157 - y) + 4.2y = 753.90
   \]

#### Step 3: Expand and solve for $ y $:
   \[
   894.9 - 5.7y + 4.2y = 753.90
   \]
   \[
   -1.5y = 753.90 - 894.9
   \]
   \[
   -1.5y = -141
   \]
   \[
   y = \frac{-141}{-1.5}
   \]
   \[
   y = 94
   \]

#### Step 4: Substitute $ y = 94 $ back into the first equation to find $ x $:
   \[
   x + 94 = 157
   \]
   \[
   x = 63
   \]

### Conclusion:
Ivan used:
- 63 pounds of type A coffee
- 94 pounds of type B coffee

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What would be the cost if the ratio of type A and type B coffee changed?
2. How would the cost per pound affect the total cost if increased by $1 for each type?
3. What if Ivan wanted to make 200 pounds of the blend? How would the quantities change?
4. How can we set up a similar system if Ivan used three types of coffee?
5. How would a discount on one type of coffee change the total cost?

**Tip:** Setting up equations based on given conditions is key to solving mixture problems like this efficiently.

Ivan's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs $5.70 per pound, and type B coffee costs $4.20 per pound. This month, Ivan made 157 pounds of the blend, for a total cost of $753.90. How many pounds of type B coffee did he use?

Learn how to solve a coffee blend problem involving two types of coffee priced at $5.70 and $4.20 per pound. This problem covers key algebraic concepts such as systems of linear equations and substitution. Discover how Ivan's 157-pound blend adds up to $753.90, and determine the amount of type B coffee used. Suitable for Grades 8-10.

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