Determine the cost of one desk and one chalkboard

Question

35 desks and 3 chalkboards cost $2082

40 desks and 2 chalkboards cost $2238

Answer 1

Question answered on 2nd posting.  No need to post a problem more than once.

Someone will look at it.

Answer 2

We have solved this problem already.

Please only post the problem once.

Thank you

Answer 3

Choose variables to represent the unknowns.

Let d = cost of desk

Let c = cost of chalkboard

 

35d + 3c = 2082   {equation 1}

40d + 2c = 2238   {equation 2}

 

Let's use elimination to solve the system of equations.

Multiply equation 1 by 2; multiply equation 2 by -3; add equations

 

   70d + 6c = 4164

-120d - 6c = -6714

--------------------------

  -50d = -2550

     d = $51 per desk

 

Plug in this value of d into one of the original equations and solve for c

to find cost of a chalkboard.

 

40d + 2c = 2238  

40(51) + 2c = 2238

Finish solving for c

Answer 4

35D + 3C = 2082

 

40D + 2 C = 2238

 

 

Multiplies the top equation by 2 and the bottom by -3

 

70D + 6C = 4164

 

-120D + -6C = -6714

 

Adding them together...

 

-50D = -2550

 

D=51

 

The desk costs $51

 

35*51 + 3*C = 2082

 

3C = 2082 - 35*51  = 297

 

C = 297/3 = 99

 

The chalkboard costs $99

 

CHECK:

  40 * 51 + 2 * 99 = 2040 + 198 = 2238

yes the answers are correct

 

the desk costs $51

the chalkboard costs $99