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mylen [45]
3 years ago
12

Ali spent $33 on 2 pairs of shorts and 3 packages of socks. Kesha spent $27 on 1 pair of shorts and 5 packages of socks. How muc

h does one of each item cost?
Mathematics
1 answer:
wolverine [178]3 years ago
7 0
X = shorts and y = socks

2x + 3y = 33
x + 5y = 27.....multiply by -2
------------
2x + 3y = 33
-2x - 10y = - 54 (result of multiplying by -2)
------------------add
-7y = - 21
y = -21/-7
y = 3

x + 5y = 27
x + 5(3) = 27
x + 15 = 27
x = 27 - 15
x = 12

so shorts (x) cost $12 and socks (y) cost $ 3 per pack

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3 0
3 years ago
A small cargo plane currently has 140 pounds of cargo aboard. In addition, n boxes weighing 45 pounds each will be brought aboar
Vika [28.1K]

Answer:

The inequality that represents this situation is: 140 + 45*n < p

Step-by-step explanation:

Since the plane already had 140 pounds on board and "n" boxes will be loaded on it, then the weigh of each box multiplied by the number of box should be the extra cargo on the plane. This extra cargo added to the previous load must be less than the limit of cargo the plane can take as shown below:

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3 0
3 years ago
Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter
mezya [45]

Answer:

Dimensions: A=a\cdot b=256

Perimiter: P=2a+2b

Minimum perimeter: [16,16]

Step-by-step explanation:

This is a problem of optimization with constraints.

We can define the rectangle with two sides of size "a" and two sides of size "b".

The area of the rectangle can be defined then as:

A=a\cdot b=256

This is the constraint.

To simplify and as we have only one constraint and two variables, we can express a in function of b as:

b=\frac{256}{a}

The function we want to optimize is the diameter.

We can express the diameter as:

P=2a+2b=2a+2*\frac{256}{a}

To optimize we can derive the function and equal to zero.

dP/da=2+2\cdot (-1)\cdot\frac{256}{a^2}=0\\\\\frac{512}{a^2}=2\\\\a=\sqrt{512/2}= \sqrt {256} =16\\\\b=256/a=256/16=16

The minimum perimiter happens when both sides are of size 16 (a square).

4 0
3 years ago
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