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Rom4ik [11]
2 years ago
6

Percy works two part-time jobs to help pay for college classes. On Monday, he works 3 hours at the library and 2 hours at the co

ffee cart and earns $36.50. On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50. His hourly wage at the library, x, and hourly wage at the coffee cart, y, can be determined using the system of equations below.
Mathematics
1 answer:
Hitman42 [59]2 years ago
8 0

Answer:

Hourly wage at the library = x = $7.5

Hourly wage at the coffee cart = y = $7

Step-by-step explanation:

Let

Hourly wage at the library = x

Hourly wage at the coffee cart = y

On Monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50.

Hence:

3x + 2y = 36.5.... Equation 1

On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50.

2x + 5y = 50...... Equation 2

Combining both Equations

3x + 2y = 36.5.... Equation 1

2x + 5y = 50...... Equation 2

We solve using Elimination method, Multiply Equation 1 by 2 and Equation 2 by 3 which are coefficients of x to eliminate x

6x + 4y = 73 .. Equation 3

6x + 15y = 150...... Equation 4

Subtract Equation 3 from Equation 4

11y = 77

y = 77/11

y = 7

Solving for x using Equation 2

2x + 5y = 50...... Equation 2

2x + 5 × 7 = 50

2x + 35 = 50

2x = 50-35

2x = 15

x = 15/2

x = 7.5

Therefore,

Hourly wage at the library = x = $7.5

Hourly wage at the coffee cart = y = $7

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{4x-2y+5z=6 <br> {3x+3y+8z=4 <br> {x-5y-3z=5
lesya692 [45]

There are three possible outcomes that you may encounter when working with these system of equations:


  •    one solution
  •    no solution
  •    infinite solutions

We are going to try and find values of x, y, and z that will satisfy all three equations at the same time. The following are the equations:

  1. 4x-2y+5z = 6
  2. 3x+3y+8z = 4
  3. x-5y-3z = 5

We are going to use elimination(or addition) method

Step 1: Choose to eliminate any one of the variables from any pair of equations.

In this case it looks like if we multiply the third equation by 4 and  subtracting it from equation 1, it will be fairly simple to eliminate the x term from the first and third equation.

So multiplying Left Hand Side(L.H.S) and Right Hand Side(R.H.S) of 3rd equation with 4 gives us a new equation 4.:

4. 4x-20y-12z = 20      

Subtracting eq. 4 from Eq. 1:

(L.HS) : 4x-2y+5z-(4x-20y-12z) = 18y+17z

(R.H.S) : 20 - 6 = 14

5. 18y+17z=14

Step 2:  Eliminate the SAME variable chosen in step 2 from any other pair of equations, creating a system of two equations and 2 unknowns.

Similarly if we multiply 3rd equation with 3 and then subtract it from eq. 2 we get:

(L.HS) : 3x+3y+8z-(3x-15y-9z) = 18y+17z

(R.H.S) : 4 - 15 = -11

6. 18y+17z = -11

Step 3:  Solve the remaining system of equations 6 and 5 found in step 2 and 1.

Now if we try to solve equations 5 and 6 for the variables y and z. Subtracting eq 6 from eq. 5 we get:

(L.HS) : 18y+17z-(18y+17z) = 0

(R.HS) : 14-(-11) = 25

0 = 25

which is false, hence no solution exists



3 0
2 years ago
3. Order the rational numbers from least to greatest:<br> 0.5, 0, - 1.5, 1, -0.5, -1
harina [27]

Answer:

-1.5,-1,0,0.5,1 is the answer

8 0
2 years ago
Stuck on this problem
zysi [14]

step 2 would be 10

step 4 would be 10x-x = 9x =7

 x = 7/9

6 0
2 years ago
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What is the value of x?
tensa zangetsu [6.8K]

Answer:

X = 5°

Step-by-step explanation:

180° on a straight line.

180 - 100 = 80 angle ABC = 80°

angle ACB is vertically opposite to the 60° given

ACB = 60°

180 - 80 - 60 = 7x+5

40 = 7x + 5

7x = 35

X = 5

6 0
3 years ago
Can someone please help me and fast I'm stuck
vovikov84 [41]

Answer:

3 5/8

Step-by-step explanation:

6 4/8 - 2 7/8 = 4 -3/8 = 3 5/8

8 0
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