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Gekata [30.6K]
3 years ago
6

A shopper purchased 8 T-shirts and 5 pairs of pants for $220. The next day he purchased 5 T-shirts and 1 pair of pants for $112.

How much does each T-shirt and each pair of pants cost?
Mathematics
1 answer:
ivanzaharov [21]3 years ago
3 0
8t + 5p = 220
5t + p = 112....multiply by -5
----------------
8t + 5p = 220
-25t - 5p = - 560 (results of multiplying by -5)
---------------add
- 17t = - 340
t = 340/17
t = 20 <== each tee shirt costs $ 20

8t + 5p = 220
8(20) + 5p = 220
160 + 5p = 220
5p = 220 - 160
5p = 60
p = 60/5
p = 12 <== each pair of pants cost $ 12
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Carlota wrote the equation y + 1 = 2 (x - 3) for the line passing through the points (-1, 3) and (2, 9). Explain and correct her
Art [367]

For this case we have the following equation:


y + 1 = 2 (x - 3)

That can be rewritten in the form y = mx + b

Where:


  • m is the slope of the line
  • b is the cut point

So, we have:


y + 1 = 2 (x - 3)\\y + 1 = 2x-6\\y = 2x-6-1\\y = 2x-7

Where:


m = 2 is the slope


b = -7 is the cut point


Carlota has the following points:


(-1, 3) and (2, 9)


To know if the line y = 2x-7 passes through these points, we must replace them in the equation and the equality must be fulfilled. So:


Point (-1, 3):


Substituting:


3 = 2 (-1) -7\\3 = -2-7

3 = -9 It's false, equality is not met. The point (-1, 3) does not go through the line.


The equation written by Carlota is erroneous, the procedure to follow is:


Given(x1, y1) = (- 1, 3) and(x2, y2) = (2, 9), we find the slope:


m=\frac{(y2-y1)}{(x2-x1)}

m=\frac{(9-3)}{(2-(-1))}

m=\frac{6}{3}

m=2

We observe that the slope found by Carlota is the same. Let's see cut point "b". For this we substitute any of the points given in the equation:


y = 2x + b

Substituting (2,9) we have:


9 = 2 (2) + b\\9 = 4 + b\\b = 9-4\\b = 5

Thus, Carlota's error was at the cut-off point. The correct equation of the line that passes through the given points is y = 2x + 5

Answer:


The correct equation of the line that passes through the given points is y = 2x + 5

Carlota's mistake was at the cutoff point


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3(2a+1)=-5(a+6)
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11a+3=-30
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Total cost of canvas required in making the tent is rupees 79128

<em><u>Solution: </u></em>

Given:

Height of the cylindrical tent = h = 3.3 m

Diameter of it's base = d = 100m

radius = \frac{diameter}{2} = \frac{100}{2} = 50

r = 50 m

<em><u>Curved surface area of cylinder:</u></em>

C.S.A = 2 \pi rh

C.S.A = 2 \times 3.14 \times 50 \times 3.3 = 1036.2

Thus Curved surface area of cylinder = 1036.2 square meter

<em><u>Curved surface area of cone:</u></em>

C.S.A = \pi rl

C.S.A = 3.14 \times 50 \times 56.4 = 8854.8

Thus Curved surface area of cone = 8854.8 square meter

<em><u>Total curved area of tent:</u></em>

⇒ curved area of cone + curved area of cylinder

\rightarrow 8854.8 + 1036.2=9891

Thus total curved area of tent = 9891 square meter

<em><u>find total cost of canvas required in making the tent:</u></em>

The cost of canvas is 8 rupees per square meter

\rightarrow \text{total cost } = 9891 \times 8 = 79128

Thus total cost of canvas required in making the tent is rupees 79128

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