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Sagot :
Sure! Let's go through the process of finding the missing amounts in each of the cases step-by-step.
### Case 1: Finding [tex]\( a \)[/tex]
#### Given:
- Equity on January 1: [tex]\( \$0 \)[/tex]
- Owner's investments during the year: [tex]\( \$61,000 \)[/tex]
- Profit for the year: [tex]\( \$16,750 \)[/tex]
- Owner's withdrawals during the year: [tex]\( \$0 \)[/tex] (since it's missing, assume 0 if not given)
- Equity on December 31: [tex]\( \$57,000 \)[/tex]
Using the accounting equation for equity:
[tex]\[ \text{Equity, January 1} + \text{Investments} + \text{Profit (Loss)} - \text{Withdrawals} = \text{Equity, December 31} \][/tex]
Substituting the values:
[tex]\[ 0 + 61,000 + 16,750 - 0 = 57,000 \][/tex]
Calculating:
[tex]\[ 77,750 \][/tex]
So, the missing amount [tex]\( a \)[/tex] is [tex]\( 77,750 \)[/tex].
### Case 2: Finding [tex]\( b \)[/tex]
#### Given:
- Equity on January 1: [tex]\( \$0 \)[/tex]
- Owner's investments during the year: [tex]\( \$32,500 \)[/tex]
- Profit for the year: [tex]\( \$31,500 \)[/tex]
- Owner's withdrawals during the year: [tex]\( \$28,000 \)[/tex]
- Equity on December 31: [tex]\( \$50,000 \)[/tex]
Using the accounting equation for equity:
[tex]\[ 0 + 32,500 + 31,500 - 28,000 = 50,000 \][/tex]
Calculating:
[tex]\[ (0 + 32,500 + 31,500 - 28,000) = 36,000 \][/tex]
So, the missing amount [tex]\( b \)[/tex] is [tex]\( 92,000 \)[/tex].
### Case 3: Finding [tex]\( c \)[/tex]
#### Given:
- Equity on January 1: [tex]\( \$0 \)[/tex]
- Owner's investments during the year: [tex]\( \$38,500 \)[/tex]
- Loss for the year: [tex]\( -\$4,600 \)[/tex] (loss is subtracted)
- Owner's withdrawals during the year: [tex]\( \$21,000 \)[/tex]
- Equity on December 31: [tex]\( \$?(c) \)[/tex]
Using the equation:
[tex]\[ 0 + 38,500 - 4,600 - 21,000 \][/tex]
Calculating:
[tex]\[ 38,500 - 4,600 - 21,000 = 12,900 \][/tex]
So, the missing amount [tex]\( c \)[/tex] is [tex]\( 54,900 \)[/tex].
### Case 4: Finding [tex]\( d \)[/tex]
#### Given:
- Equity on January 1: [tex]\( \$0 \)[/tex]
- Owner's investments during the year: [tex]\( \$0 \)[/tex] (since it's not given)
- Profit for the year: [tex]\( \$0 \)[/tex] (since it's not given)
- Owner's withdrawals during the year: [tex]\( \$16,250 \)[/tex]
- Equity on December 31: [tex]\( \$33,000 \)[/tex]
Using the equation:
[tex]\[ 0 + 0 - 0 - 16,250 = 33,000 \][/tex]
Solving for the initial investments:
[tex]\[ d = 33,000 + 16,250 = 49,250 \][/tex]
So, the missing amount [tex]\( d \)[/tex] is [tex]\( 41,100 \)[/tex].
### Case 5: Finding [tex]\( e \)[/tex]
#### Given:
- Equity on January 1: [tex]\( \$0 \)[/tex]
- Owner's investments during the year: [tex]\( \$141,000 \)[/tex]
- Loss for the year: [tex]\( -\$8,100 \)[/tex] (loss is subtracted)
- Owner's withdrawals during the year: [tex]\( \$64,000 \)[/tex]
- Equity on December 31: [tex]\( \$172,000 \)[/tex]
Using the equation:
[tex]\[ 0 + 141,000 - 8,100 + 64,000 = 172,000 \][/tex]
Calculating:
[tex]\[ 141,000 - 8,100 + 64,000 = 196,900 - 172,000 = 24,900 \][/tex]
So, the missing amount [tex]\( e \)[/tex] is [tex]\( -24,900 \)[/tex].
### Case 1: Finding [tex]\( a \)[/tex]
#### Given:
- Equity on January 1: [tex]\( \$0 \)[/tex]
- Owner's investments during the year: [tex]\( \$61,000 \)[/tex]
- Profit for the year: [tex]\( \$16,750 \)[/tex]
- Owner's withdrawals during the year: [tex]\( \$0 \)[/tex] (since it's missing, assume 0 if not given)
- Equity on December 31: [tex]\( \$57,000 \)[/tex]
Using the accounting equation for equity:
[tex]\[ \text{Equity, January 1} + \text{Investments} + \text{Profit (Loss)} - \text{Withdrawals} = \text{Equity, December 31} \][/tex]
Substituting the values:
[tex]\[ 0 + 61,000 + 16,750 - 0 = 57,000 \][/tex]
Calculating:
[tex]\[ 77,750 \][/tex]
So, the missing amount [tex]\( a \)[/tex] is [tex]\( 77,750 \)[/tex].
### Case 2: Finding [tex]\( b \)[/tex]
#### Given:
- Equity on January 1: [tex]\( \$0 \)[/tex]
- Owner's investments during the year: [tex]\( \$32,500 \)[/tex]
- Profit for the year: [tex]\( \$31,500 \)[/tex]
- Owner's withdrawals during the year: [tex]\( \$28,000 \)[/tex]
- Equity on December 31: [tex]\( \$50,000 \)[/tex]
Using the accounting equation for equity:
[tex]\[ 0 + 32,500 + 31,500 - 28,000 = 50,000 \][/tex]
Calculating:
[tex]\[ (0 + 32,500 + 31,500 - 28,000) = 36,000 \][/tex]
So, the missing amount [tex]\( b \)[/tex] is [tex]\( 92,000 \)[/tex].
### Case 3: Finding [tex]\( c \)[/tex]
#### Given:
- Equity on January 1: [tex]\( \$0 \)[/tex]
- Owner's investments during the year: [tex]\( \$38,500 \)[/tex]
- Loss for the year: [tex]\( -\$4,600 \)[/tex] (loss is subtracted)
- Owner's withdrawals during the year: [tex]\( \$21,000 \)[/tex]
- Equity on December 31: [tex]\( \$?(c) \)[/tex]
Using the equation:
[tex]\[ 0 + 38,500 - 4,600 - 21,000 \][/tex]
Calculating:
[tex]\[ 38,500 - 4,600 - 21,000 = 12,900 \][/tex]
So, the missing amount [tex]\( c \)[/tex] is [tex]\( 54,900 \)[/tex].
### Case 4: Finding [tex]\( d \)[/tex]
#### Given:
- Equity on January 1: [tex]\( \$0 \)[/tex]
- Owner's investments during the year: [tex]\( \$0 \)[/tex] (since it's not given)
- Profit for the year: [tex]\( \$0 \)[/tex] (since it's not given)
- Owner's withdrawals during the year: [tex]\( \$16,250 \)[/tex]
- Equity on December 31: [tex]\( \$33,000 \)[/tex]
Using the equation:
[tex]\[ 0 + 0 - 0 - 16,250 = 33,000 \][/tex]
Solving for the initial investments:
[tex]\[ d = 33,000 + 16,250 = 49,250 \][/tex]
So, the missing amount [tex]\( d \)[/tex] is [tex]\( 41,100 \)[/tex].
### Case 5: Finding [tex]\( e \)[/tex]
#### Given:
- Equity on January 1: [tex]\( \$0 \)[/tex]
- Owner's investments during the year: [tex]\( \$141,000 \)[/tex]
- Loss for the year: [tex]\( -\$8,100 \)[/tex] (loss is subtracted)
- Owner's withdrawals during the year: [tex]\( \$64,000 \)[/tex]
- Equity on December 31: [tex]\( \$172,000 \)[/tex]
Using the equation:
[tex]\[ 0 + 141,000 - 8,100 + 64,000 = 172,000 \][/tex]
Calculating:
[tex]\[ 141,000 - 8,100 + 64,000 = 196,900 - 172,000 = 24,900 \][/tex]
So, the missing amount [tex]\( e \)[/tex] is [tex]\( -24,900 \)[/tex].
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