The Peterson family takes their clothes to the local cleaners. The table below gives the number of coats, shirts, and dresses they had cleaned over the course of three months. They had no other items cleaned there.
(January) 5 coats, 5 shirts, 6 dresses
(February) 1 coat, 8 shirts, 6 dresses
(March) 3 coats, 3 shirts, 2 dresses
If they spent
$77
at the cleaners in January,
$67
in February, and
$43
in March, what is the cost to have each item cleaned?
Cost to have a coat cleaned?
Cost to have a shirt cleaned?
Cost to have a dress cleaned?
Do you do matrix algebra on your calculator?
coats, shirts, dresses, cost
in augmented matrix form:
5,5,6,77
1,8,6,67
3,3,2,43
Now if you want to do it manually as a 3x3 set
5x+5y+6d=77 and so on, then solve it with pencil and paper. The augmented matrix is much faster..
deyh
To find the cost to have each item cleaned, we need to divide the total amount spent in each month by the number of items cleaned in that month.
Let's calculate the cost to have a coat cleaned:
In January, the Peterson family had 5 coats cleaned, and they spent $77. Therefore, the cost to have a coat cleaned in January is $77 divided by 5, which is $15.40.
In February, they had 1 coat cleaned, and they spent $67. Therefore, the cost to have a coat cleaned in February is $67 divided by 1, which is $67.
In March, they had 3 coats cleaned, and they spent $43. Therefore, the cost to have a coat cleaned in March is $43 divided by 3, which is $14.33.
To find the average cost to have a coat cleaned, we add up the costs for each month and divide by the total number of coats cleaned:
($77 + $67 + $43) / (5 + 1 + 3) = $187 / 9 = $20.78
So, the average cost to have a coat cleaned is approximately $20.78.
Now let's calculate the cost to have a shirt cleaned:
In January, the Peterson family had 5 shirts cleaned, and they spent $77. Therefore, the cost to have a shirt cleaned in January is $77 divided by 5, which is $15.40.
In February, they had 8 shirts cleaned, and they spent $67. Therefore, the cost to have a shirt cleaned in February is $67 divided by 8, which is $8.38.
In March, they had 3 shirts cleaned, and they spent $43. Therefore, the cost to have a shirt cleaned in March is $43 divided by 3, which is $14.33.
To find the average cost to have a shirt cleaned, we add up the costs for each month and divide by the total number of shirts cleaned:
($77 + $67 + $43) / (5 + 8 + 3) = $187 / 16 = $11.69
So, the average cost to have a shirt cleaned is approximately $11.69.
Finally, let's calculate the cost to have a dress cleaned:
In January, the Peterson family had 6 dresses cleaned, and they spent $77. Therefore, the cost to have a dress cleaned in January is $77 divided by 6, which is $12.83.
In February, they had 6 dresses cleaned, and they spent $67. Therefore, the cost to have a dress cleaned in February is $67 divided by 6, which is $11.17.
In March, they had 2 dresses cleaned, and they spent $43. Therefore, the cost to have a dress cleaned in March is $43 divided by 2, which is $21.50.
To find the average cost to have a dress cleaned, we add up the costs for each month and divide by the total number of dresses cleaned:
($77 + $67 + $43) / (6 + 6 + 2) = $187 / 14 = $13.36
So, the average cost to have a dress cleaned is approximately $13.36.
To summarize:
- The average cost to have a coat cleaned is approximately $20.78.
- The average cost to have a shirt cleaned is approximately $11.69.
- The average cost to have a dress cleaned is approximately $13.36.
To find the cost of having each item cleaned, we need to divide the total amount spent in each month by the respective number of coats, shirts, and dresses cleaned.
In January, the Peterson family spent $77 to have their clothes cleaned. They had 5 coats, 5 shirts, and 6 dresses cleaned.
To find the cost of each coat, we divide $77 by 5:
Cost of a coat = $77 / 5 = $15.4
To find the cost of each shirt, we divide $77 by 5:
Cost of a shirt = $77 / 5 = $15.4
To find the cost of each dress, we divide $77 by 6:
Cost of a dress = $77 / 6 ≈ $12.8
In February, the Peterson family spent $67 to have their clothes cleaned. They had 1 coat, 8 shirts, and 6 dresses cleaned.
To find the cost of the coat, we divide $67 by 1:
Cost of a coat = $67 / 1 = $67
To find the cost of each shirt, we divide $67 by 8:
Cost of a shirt = $67 / 8 ≈ $8.38
To find the cost of each dress, we divide $67 by 6:
Cost of a dress = $67 / 6 ≈ $11.17
In March, the Peterson family spent $43 to have their clothes cleaned. They had 3 coats, 3 shirts, and 2 dresses cleaned.
To find the cost of each coat, we divide $43 by 3:
Cost of a coat = $43 / 3 ≈ $14.33
To find the cost of each shirt, we divide $43 by 3:
Cost of a shirt = $43 / 3 ≈ $14.33
To find the cost of each dress, we divide $43 by 2:
Cost of a dress = $43 / 2 = $21.5
So, the cost to have each item cleaned is as follows:
- Cost to have a coat cleaned: $15.4, $67, $14.33 (for January, February, and March respectively)
- Cost to have a shirt cleaned: $15.4, $8.38, $14.33 (for January, February, and March respectively)
- Cost to have a dress cleaned: $12.8, $11.17, $21.5 (for January, February, and March respectively)