T=5c + 12f
A manufacturer shipped units of a certain product to two locations. The equation above shows the total shipping cost T, in dollars, for shipping c units to the closer location and shipping cost was $47,000 and 3000 units were shipped to the farther location, how many units were shipped to the closer location ?

Options

A. 1100
B. 2400
C. 2200
D. 5000

Explanation

To find the number of units shipped to the closer location, we can follow these steps:

1. **Identify the given information**:
- The total shipping cost \( T = 47,000 \) dollars.
- The number of units shipped to the farther location \( f = 3000 \).
- The shipping cost equation is \( T = 5c + 12f \).

2. **Substitute the known values into the equation**:
\[ 47,000 = 5c + 12(3000) \]

3. **Calculate the cost for shipping to the farther location**:
\[ 12 \times 3000 = 36,000 \]
So, the equation becomes:
\[ 47,000 = 5c + 36,000 \]

4. **Isolate the term with \( c \)**:
Subtract \( 36,000 \) from both sides:
\[ 47,000 - 36,000 = 5c \]
\[ 11,000 = 5c \]

5. **Solve for \( c \)**:
Divide both sides by \( 5 \):
\[ c = \frac{11,000}{5} = 2,200 \]

Thus, the number of units shipped to the closer location is **2,200**.