##### Question

# Your company produces two models of bicycles: Model A and Model B

Your company produces two models of bicycles: Model A and Model B. Model A takes 2 hours to assemble, where Model B takes 3 hours to assemble. Model A costs $25 to make per bike where Model B costs $30 to make per bike. If your company has a total of 34 hours and $350 available per day for these two models, how many of each model can be made in a day?

Solve using Elimination Method:

Equation:

120x+180y = 21,600 hours assembling per day

$25x+$30y = $750 costs

first equation:

120x + 180y = 21,600

second equation

(-5) 25 + (-5) 30y = (-5) 750

elimination 245x + 330y = -17,850

substitute back in to equation

120x + 180y ( ) = 21,600

x = bikes per day

I need help solving this equation with the steps

## Solutions

##### Expert Solution

Your company produces two models of bicycles: Model A and Model B.

Model A takes 2 hours to assemble, where Model B takes 3 hours to assemble.

Model A costs $25 to make per bike where Model B costs $30 to make per bike.

If your company has a total of 34 hours and $350 available per day for these

two models, how many of each model can be made in a day?

Solve using Elimination Method:

:

I am not sure what you are doing here, but you are making it way more complicated than it is:

:

Let a = no. of A bikes

Let b = no. of B bikes

:

2a + 3b = 34; total hrs available

:

25a + 30b = 350; total cost available

;

Multiply the 1st equation by 10 and subtract from the above equation

25a + 30b = 350

20a + 30b = 340

——————subtraction eliminates b

5a = 10

a = 2 ea A models

:

use the time equation to find b

2(2) + 3b = 34

4 + 3b = 34

3b = 34 – 4

3b = 30

b = {{{30/3}}}

b = 10 ea B models per day

;

:

Check solution in the cost equation

25(2) + 30(10) = $350 confirms our solution

Model A takes 2 hours to assemble, where Model B takes 3 hours to assemble.

Model A costs $25 to make per bike where Model B costs $30 to make per bike.

If your company has a total of 34 hours and $350 available per day for these

two models, how many of each model can be made in a day?

Solve using Elimination Method:

:

I am not sure what you are doing here, but you are making it way more complicated than it is:

:

Let a = no. of A bikes

Let b = no. of B bikes

:

2a + 3b = 34; total hrs available

:

25a + 30b = 350; total cost available

;

Multiply the 1st equation by 10 and subtract from the above equation

25a + 30b = 350

20a + 30b = 340

——————subtraction eliminates b

5a = 10

a = 2 ea A models

:

use the time equation to find b

2(2) + 3b = 34

4 + 3b = 34

3b = 34 – 4

3b = 30

b = {{{30/3}}}

b = 10 ea B models per day

;

:

Check solution in the cost equation

25(2) + 30(10) = $350 confirms our solution

answered by: Sharon