Questions: A bagel store orders cream cheese from three suppliers, Cheesy Cream Corp. (CCC), Super Smooth Sons (S5), and Bager'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 6,035. Given that the store ordered the same amount from CCC and BBF, how many tons of cream cheese were ordered from each supplier? Cheesy Cream Corp. tons Super Smooth Sons tons Bager's Best Friend Co. tons

A bagel store orders cream cheese from three suppliers, Cheesy Cream Corp. (CCC), Super Smooth Sons (S5), and Bager'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 6,035. Given that the store ordered the same amount from CCC and BBF, how many tons of cream cheese were ordered from each supplier?
Cheesy Cream Corp. tons
Super Smooth Sons tons
Bager's Best Friend Co. tons

Transcript text: A bagel store orders cream cheese from three suppliers, Cheesy Cream Corp. (CCC), Super Smooth \& Sons (S\$5), and Bager'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 $\$ 6,035$. Given that the store ordered the same amount from CCC and BBF, how many tons of cream cheese were ordered from each supplier? Cheesy Cream Corp. $\qquad$ tons Super Smooth \& Sons $\qquad$ tons Bager's Best Friend Co. $\qquad$ tons

Solution

Solution Steps

Step 1: Set Up the Equations

We start by defining the variables for the tons of cream cheese ordered from each supplier:

Let $ ccc $ be the tons ordered from Cheesy Cream Corp. (CCC).
Let $ sss $ be the tons ordered from Super Smooth & Sons (S\$5).
Let $ bbf $ be the tons ordered from Bager's Best Friend Co. (BBF).

From the problem statement, we can set up the following equations:

Total quantity of cream cheese ordered: \[ ccc + sss + bbf = 100 \]
Total cost of the cream cheese: \[ 80 \cdot ccc + 50 \cdot sss + 65 \cdot bbf = 6035 \]
The store ordered the same amount from CCC and BBF: \[ ccc = bbf \]

Step 2: Solve the Equations

By substituting $ ccc $ with $ bbf $ in the first equation, we can rewrite it as: \[ bbf + sss + bbf = 100 \implies 2 \cdot bbf + sss = 100 \]

From this, we can express $ sss $ in terms of $ bbf $: \[ sss = 100 - 2 \cdot bbf \]

Next, substituting $ ccc $ and $ sss $ into the cost equation gives: \[ 80 \cdot bbf + 50 \cdot (100 - 2 \cdot bbf) + 65 \cdot bbf = 6035 \]

Simplifying this equation: \[ 80 \cdot bbf + 5000 - 100 \cdot bbf + 65 \cdot bbf = 6035 \] \[ (80 + 65 - 100) \cdot bbf + 5000 = 6035 \] \[ 45 \cdot bbf + 5000 = 6035 \] \[ 45 \cdot bbf = 6035 - 5000 \] \[ 45 \cdot bbf = 1035 \] \[ bbf = \frac{1035}{45} = 23 \]

Step 3: Calculate the Tons Ordered from Each Supplier

Now that we have $ bbf = 23 $, we can find $ ccc $ and $ sss $: \[ ccc = bbf = 23 \] \[ sss = 100 - 2 \cdot bbf = 100 - 2 \cdot 23 = 54 \]