A bagel store orders cream cheese from three suppliers, Cheesy Cream Corp. (CCC), Super Smooth & Sons (SSS), and Bagel's Best Friend Co. (BBF). One month, the total order of cheese came to 100 tons. (The store does do a booming trade.) The costs were $80, $50 and $65 per ton from the three suppliers respectively, with the total cost amounting to $6,170. Given that the store ordered the same amount from CCC and BBF, how many tons of cream cheese were ordered from each supplier?

Let the amount of cream cheese ordered from each supplier be as follows:

- $ x $ tons from Cheesy Cream Corp (CCC),
- $ y $ tons from Super Smooth & Sons (SSS),
- $ x $ tons from Bagel's Best Friend Co. (BBF).

We are given the following information:

1. The total order was 100 tons:
\[
x + y + x = 100 \quad \text{(since the amounts from CCC and BBF are the same)}
\]
This simplifies to:
\[
2x + y = 100 \quad \text{(Equation 1)}.
\]

2. The costs per ton are $80, $50, and $65 for CCC, SSS, and BBF respectively, and the total cost was $6,170. This gives us the cost equation:
\[
80x + 50y + 65x = 6170
\]
This simplifies to:
\[
145x + 50y = 6170 \quad \text{(Equation 2)}.
\]

Now, we solve these two equations simultaneously.

### Step 1: Solve Equation 1 for $ y $
From Equation 1:
\[
2x + y = 100 \implies y = 100 - 2x.
\]

### Step 2: Substitute $ y $ into Equation 2
Substitute $ y = 100 - 2x $ into Equation 2:
\[
145x + 50(100 - 2x) = 6170
\]
Simplify:
\[
145x + 5000 - 100x = 6170
\]
\[
45x + 5000 = 6170
\]
\[
45x = 1170
\]
\[
x = \frac{1170}{45} = 26.
\]

### Step 3: Find $ y $
Substitute $ x = 26 $ into $ y = 100 - 2x $:
\[
y = 100 - 2(26) = 100 - 52 = 48.
\]

### Final Answer:
- $ x = 26 $ tons from CCC,
- $ y = 48 $ tons from SSS,
- $ x = 26 $ tons from BBF.

Thus, the store ordered 26 tons from both Cheesy Cream Corp. and Bagel's Best Friend Co., and 48 tons from Super Smooth & Sons.

Would you like more details or have any questions about the solution?

Here are five related questions for further practice:
1. If the price of cream cheese from SSS increased to $60 per ton, how would that affect the total cost?
2. What is the total cost if the store decided to order 10 more tons from SSS and 10 fewer tons from CCC and BBF equally?
3. How would the amounts ordered change if the store wanted to spend exactly $6,000 while keeping the total tonnage the same?
4. If the price per ton from CCC dropped to $75, how much would the new total cost be?
5. What percentage of the total tonnage is ordered from SSS?

**Tip**: When solving systems of equations, it's helpful to simplify as much as possible before substituting values!

A bagel store orders cream cheese from three suppliers, Cheesy Cream Corp. (CCC), Super Smooth & Sons (SSS), and Bagel's Best Friend Co. (BBF). One month, the total order of cheese came to 100 tons. The costs were $80, $50 and $65 per ton from the three suppliers respectively, with the total cost amounting to $6,170. Given that the store ordered the same amount from CCC and BBF, how many tons of cream cheese were ordered from each supplier?

Learn how to solve a system of simultaneous equations to determine the amount of cream cheese ordered from three suppliers. This algebra problem involves solving two linear equations based on total cost and total quantity. Suitable for students in Grades 8-10.

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