Chairs produced by second shift.

Question

a company produced 2320 chairs in a day with two shifts. the second shift produced 60 chairs fewer then four-thirds of the number of chairs the first shift made. how many chairs did the second shift make?

Answer 1

Let's first name our variables: x and y for the two shifts. Here's what we know:

x + y = 2320 (2320 chairs made in a day)

y = ⁴/₃x - 60 (the second shift made 60 less than ⁴/₃ of the first)

 

From here we have a substitution method as we have a value for one of our variables:

x + (⁴/3x - 60) = 2320

We need to add like terms.

1 ⇒ ³/₃

⁷/₃x - 60 = 2320

 

Now we need to isolate x. Start by moving the constant over by adding 60 to both sides:

⁷/₃x = 2380

Now multiply both sides by 3/7 to isolate x

x = 2380 * ³/₇

x = 340 * 7

x = 1020 chairs

 

Now that we know x, we can solve for y:

y = ⁴/₃ * 1020 - 60

y = 1360 - 60

y = 1300 chairs

Now to check our answer:

1020 + 1300 = 2320

2320 = 2320

Answer 2

1st shift : x chairs
2nd shift : (4/3)x - 60


x + (4/3)x - 60 = 2320

(3/3)x + (4/3)x - 60 = 2320

(7/3)x - 60 = 2320

(7/3)x = 2320 + 60

(7/3) x = 2380

(3/7)(7/3)x = (3/7)(2380)

x = 3(340) = 1020


2nd shift = (4/3)(1020) - 60 = 4(340) - 60 = 1360 - 60 = 1300

1st shift :  x chairs

2nd shift :  (4/3)x - 60

 

 

x + (4/3)x - 60 = 2320

 

(3/3)x + (4/3)x - 60 = 2320

 

(7/3)x - 60 = 2320

 

(7/3)x = 2320 + 60

 

(7/3) x = 2380

 

(3/7)(7/3)x = (3/7)(2380)

 

x = 3(340) = 1020

 

 

2nd shift = (4/3)(1020) - 60 = 4(340) - 60 = 1360 - 60 = 1300