What are the values of each Halloween icon? (Math Logic Puzzles) (78 POINTS)

The prices of commodities X,Y,Z are respectively x, y, z, rupees per unit. Mr. A purchases 4 units of Z and sells 3 units of X a

liubo4ka [24]

Answer:

$(x,y,z)=(1477, 1464, 1437)$

Step-by-step explanation:

Consider the selling of the units positive earning and the purchasing of the units negative earning.

Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y
Mr.A earns Rs6000

So, the equation would be

$3x + 5y - 4z = 6000$

Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z
Mr B neither lose nor gain meaning he has made 0₹

hence,

$2x - 3y + z = 0$

Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z
Mr.C earns 13000₹

therefore,

$- x + 4y + 6z = 13000$

Thus our system of equations is

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

<u>Solving </u><u>the </u><u>system </u><u>of </u><u>equations</u><u>:</u>

we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\end{cases}\\\begin{cases}2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

Now solve the equation accordingly:

$\implies\begin{cases}11x-7y=6000\\-13x+22y=13000\end{cases}$

Solving the equation for x and y yields:

$\implies\begin{cases}x= \dfrac{223000}{151}\\\\y= \dfrac{221000}{151}\end{cases}$

plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,

$\implies z= \dfrac{217000}{151}$

Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437

6 0

2 years ago

A bag contains 9 marbles: 4 are green, 3 are red, and 2 are blue. Deshaun chooses a marble at random, and without putting it bac

nexus9112 [7]

Step-by-step explanation:

Total marbles = 9 + 4 + 3 + 2 = 18

Probability of both red marbles = 3 / 18 = 1/6

4 0

3 years ago

In Euclidean geometry, the sum of the measures of the interior angles of a pentagon is 540°. Predict how the sum of the measures

Blizzard [7]

In Euclidean geometry, the sum of the measures of the interior anlges of a pentagon is 540°.

The sum of the measures of the interior angles of a pentagon would be different in spherical geometry because A.) THE SUM WOULD BE GREATER THAN 540°

6 0

3 years ago

Two numbers rolled can be added to get a sum. Find P(sum is even.)

azamat

When you roll two numbers you have four kinds of outcomes: EE, EO, OE, OO (where E = even, O = odd).

You get an even sum only if you sum two numbers that are both even or both odd, therefore the outcomes wanted are two: EE and OO.

Therefore:
P(sum is even) = 2 / 4 = 0.5

Hence, there is a 50% probability that, when you roll two numbers, their sum will be even.

6 0

3 years ago

Write an equation perpendicular to y= 1 -x+ 9 that passes through the point (-2,-2). 5

lukranit [14]

<u>ANSWER</u><u> </u><u>:</u><u> </u>Hii friends follow me and give me brainliest ok by

6 0

3 years ago