Insert mathematical symbols in the place of '? to get the result of the given equation as 87: (150? 2)?2)?10 =87

Options

A. `+ ,xx,xx`
B. `+ -: , -:`
C. `- , xx ,-:`
D. `-:, + ,+`

Answer

To solve the equation \( 150?2?2?10 = 87 \) by inserting mathematical symbols in place of '?', we will go through the following steps:

### Step 1: Understanding the Equation
We need to find symbols that can replace the '?' in the equation \( 150?2?2?10 \) so that the entire expression equals 87.

### Step 2: Testing Different Combinations
We will try different combinations of mathematical operations (addition, subtraction, multiplication, and division) to see which one gives us the result of 87.

### Step 3: Trying the First Combination
Let's start with the combination of operations:
- Replace the first '?': \( 150 + 2 \)
- Replace the second '?': \( 2 + 2 \)
- Replace the third '?': \( 10 \)

This gives us:
\[ 150 + 2 \times 2 \times 10 \]
Calculating this:
\[ 150 + 2 \times 2 = 150 + 4 = 154 \]
Then:
\[ 154 \times 10 = 1540 \quad \text{(not equal to 87)} \]

### Step 4: Trying Another Combination
Now, let's try:
- Replace the first '?': \( 150 + 2 \)
- Replace the second '?': \( 2 \div 2 \)
- Replace the third '?': \( 10 \)

This gives us:
\[ 150 + 2 \div 2 + 10 \]
Calculating this:
\[ 150 + 1 + 10 = 161 \quad \text{(not equal to 87)} \]

### Step 5: Trying a Different Approach
Now, let's try:
- Replace the first '?': \( 150 \div 2 \)
- Replace the second '?': \( 2 + 2 \)
- Replace the third '?': \( 10 \)

This gives us:
\[ 150 \div 2 + 2 + 10 \]
Calculating this:
\[ 75 + 2 + 10 = 87 \quad \text{(this works!)} \]

### Step 6: Finalizing the Solution
The correct symbols to replace '?' are:
- First '?': \( \div \)
- Second '?': \( + \)
- Third '?': \( + \)

Thus, the complete equation is:
\[ 150 \div 2 + 2 + 10 = 87 \]

### Conclusion
The correct answer is:
\[ 150 \div 2 + 2 + 10 = 87 \]