Simplify and find '?'
`48 \sqrt{?}+32 \sqrt{?}=\mathbf{3 2 0}`

Options

A. A) 4
B. B) 8
C. C) 16
D. D) 32

Answer

To solve the equation \( 48 \sqrt{?} + 32 \sqrt{?} = 320 \), we will follow these steps:

### Step 1: Substitute the Question Mark
Let \( ? = x \). Therefore, the equation becomes:
\[ 48 \sqrt{x} + 32 \sqrt{x} = 320 \]

### Step 2: Combine Like Terms
Combine the terms on the left side:
\[ (48 + 32) \sqrt{x} = 320 \]
\[ 80 \sqrt{x} = 320 \]

### Step 3: Isolate \( \sqrt{x} \)
Now, divide both sides by 80:
\[ \sqrt{x} = \frac{320}{80} \]
\[ \sqrt{x} = 4 \]

### Step 4: Square Both Sides
To eliminate the square root, square both sides:
\[ x = 4^2 \]
\[ x = 16 \]

### Conclusion
The value of the question mark \( ? \) is \( 16 \).

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