A transport company charges an artist $6 for each picture safety delivered but had to pay the artist $21 for every picture damaged during the delivery.if. The artist paid a total of $6246.66 inclusive of 7 percent GST to the company for the delivery of 1000 pictures were damaged on the way .
Let's break down the problem step-by-step:
Step 1: Understanding the given information:
- The transport company charges the artist $6 for each picture safely delivered.
- The transport company pays the artist $21 for every picture damaged during delivery.
- The artist paid a total of $6246.66, inclusive of 7 percent GST, to the company.
- 1000 pictures were damaged during delivery.
Step 2: Calculating the amount paid for safely delivered pictures:
Let's assume the number of pictures safely delivered is 'x'.
The transport company charges $6 for each picture safely delivered, so the total amount paid for safely delivered pictures is 6x.
Step 3: Calculating the amount paid for damaged pictures:
The transport company pays the artist $21 for every picture damaged during delivery.
Given that 1000 pictures were damaged, the total amount paid for damaged pictures is 21 * 1000.
Step 4: Including the GST:
The artist paid a total of $6246.66, inclusive of 7 percent GST.
To calculate the amount without GST, we need to divide $6246.66 by 1.07 (1 + 7% as a decimal).
Step 5: Setting up the equation:
The amount paid for safely delivered pictures (6x) plus the amount paid for damaged pictures (21 * 1000) should equal the amount without GST ($6246.66 / 1.07).
6x + (21 * 1000) = $6246.66 / 1.07
Step 6: Solving the equation:
Let's calculate the amount without GST first:
Amount_without_GST = $6246.66 / 1.07
Now, subtract the amount paid for damaged pictures from the amount without GST:
Amount_without_GST - (21 * 1000) = 6x
Substituting the calculated value for Amount_without_GST:
Amount_without_GST = $6246.66 / 1.07
Amount_without_GST - (21 * 1000) = 6x
Solving this equation will give us the value of x, which represents the number of pictures safely delivered.
To find the cost of delivering each picture safely, we can use the equation:
Cost per safely delivered picture = Total cost - Cost of damaged pictures
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Number of safely delivered pictures
We know that the total cost, inclusive of 7% GST, paid by the artist is $6246.66.
Step 1: Calculating the total cost before GST:
Let X be the total cost before GST.
Total cost before GST = X
Step 2: Calculating the GST amount:
GST amount = 7% of X
= 0.07 * X
Step 3: Calculating the total cost including GST:
Total cost including GST = Total cost before GST + GST amount
= X + 0.07 * X
= 1.07 * X
Step 4: Calculating the total cost of damaged pictures:
Total cost of damaged pictures = Number of damaged pictures * Cost per damaged picture
= 1000 * $21
Step 5: Calculating the total cost of safely delivered pictures:
Total cost of safely delivered pictures = Total cost including GST - Total cost of damaged pictures
= 1.07 * X - 1000 * $21
Given that X is the cost of delivering each picture safely, we can set up the equation:
1000 * X + 1.07 * X = $6246.66 + 1000 * $21
Simplifying the equation:
1000X + 1.07X = $6246.66 + $21000
1001.07X = $27246.66
X = $27246.66 / 1001.07
X ≈ $27.20 (rounded to the nearest cent)
Therefore, the cost of delivering each picture safely is approximately $27.20.