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If 112 ones + 12 thousand = 11012 + .......

If 112 ones + 12 thousand = 11012 + ....... tens, then the number in the blank space is

A

111

B

112

C

101

D

110

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the value that goes in the blank space in the equation: \[ 112 \text{ ones} + 12,000 = 11,012 + \text{ (blank)} \text{ tens} \] Let's break it down step by step: ### Step 1: Convert the ones and thousands to their numerical values - **112 ones** can be written as: \[ 112 \times 1 = 112 \] - **12 thousand** can be written as: \[ 12,000 \] ### Step 2: Combine the values Now, we add the values we calculated: \[ 112 + 12,000 = 12,112 \] ### Step 3: Set up the equation We now have: \[ 12,112 = 11,012 + \text{ (blank)} \text{ tens} \] Let the number of tens in the blank space be \( x \). Therefore, we can express the tens as: \[ 10x \] Now, we rewrite the equation: \[ 12,112 = 11,012 + 10x \] ### Step 4: Isolate \( 10x \) To find \( 10x \), we subtract \( 11,012 \) from both sides: \[ 12,112 - 11,012 = 10x \] Calculating the left side: \[ 1,100 = 10x \] ### Step 5: Solve for \( x \) Now, we divide both sides by 10 to find \( x \): \[ x = \frac{1,100}{10} = 110 \] ### Conclusion The number in the blank space is: \[ \boxed{110} \]
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