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gooby1324
30.06.2021 •
Mathematics
2. The prices, in dollars per unit, of the three commodities X, Y and Z are x, y and z,
respectively
Person A purchases 4 units of Z and sells 3 units of X and 3 units of Y.
Person B purchases 3 units of Y and sells 2 units of X and 1 unit of Z.
Person C purchases 1 unit of X and sells 4 units of Y and 6 units of Z.
In the process, A, B and C earn $40, $50, and $130, respectively.
a) Find the prices of the commodities X, Y, and Z by solving a system of linear
equations (note that selling the units is positive earning and buying the units is
negative earning).
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Ответ:
Price of X is $24.81
Price of Y is $3.66
Price of Z is $11.36
Step-by-step explanation:
for person A, we know that earns $40, then we can write the equation:
-4*z + 3*x + 3*y = $40
For person B, we know that earns $50, then:
1*z + 2*x - 3*y = $50
For person C, we know that earns $130, then:
6*z - 1*x + 4*y = $130
Then we have a system of equations:
-4*z + 3*x + 3*y = $40
1*z + 2*x - 3*y = $50
6*z - 1*x + 4*y = $130
To solve the system, we need to isolate one of the variables in one of the equations.
Let's isolate z in the second equation:
z = $50 - 2*x + 3*y
now we can replace this in the other two equations:
-4*z + 3*x + 3*y = $40
6*z - 1*x + 4*y = $130
So we get:
-4*($50 - 2*x + 3*y) + 3*x + 3*y = $40
6*($50 - 2*x + 3*y) - 1*x + 4*y = $130
Now we need to simplify both of these, so we get:
-$200 + 11x - 9y = $40
$350 - 13*x + 28*y = $130
Now again, we need to isolate one of the variables in one of the equations.
Let's isolate x in the first one:
-$200 + 11x - 9y = $40
11x - 9y = $40 + $200 = $240
11x = $240 + 9y
x = ($240 + 9y)/11
Now we can replace this in the other equation:
$350 - 13*x + 28*y = $130
$350 - 13*($240 + 9y)/11 + 28*y = $130
Now we can solve this for y.
- 13*($240 + 9y)/11 + 28*y = $130 - $350 = -$220
-13*$240 - (13/11)*9y + 28y = - $220
y*(28 - (9*13/1) ) = -$220 + (13/11)*$240
y = ( (13/11)*$240 - $220)/(28 - (9*13/1) ) = $3.66
We know that:
x = ($240 + 9y)/11
Replacing the value of y, we get:
x = ($240 + 9*$3.66)/11 = $24.81
And the equation of z is:
z = $50 - 2*x + 3*y = $50 - 2* $24.81 + 3*$3.66 = $11.36
Then:
Price of X is $24.81
Price of Y is $3.66
Price of Z is $11.36
Ответ:
y= x-28; The missing numbers are 9 and
Step-by-step explanation:
As an example in the table it has 32 as x and 4 as y. 32-28 =4