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Question

8 Foos and 14 Bars can build 510 Fartz in 10 hours.

13 Foos and 6 Bars can build 492 Fartz in 12 hours.

At what rates do Foos & Bars individually build Fartz?

Express your answers in Fartz per hour.

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Foos build 2 fartz per hour and Bars build 2.5 fartz per hour.

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f = foo

b = bar

f/h = Fartz per hour

8f + 14b = 51 f/h

13f + 6b = 41 f/h

51/41 = 1.2439

multiply 13f and 6b by this number so that both sides equal 51 f/h and you can set them equal to each other:

8f + 14b = 51 f/h

16.1707f + 7.463b = 51 f/h

thus:

(8f + 14b) = (16.1707f + 7.463b)

subtract 8f and 14b from both sides

0 = 8.1707f - 6.537b

add 6.537b to both sides

6.537b = 8.1707f

multiply by a thousand for simplicity

6537b =approx= 8171f

add them together: 14708 total

divide by 51 to get 288.392

so now divide 6537 by 288.392 = 22.667 f/h for Bars

divide 8171 by 288.392 = 28.333 f/h for Foos

Am I even close? lol

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f = foo

b = bar

f/h = Fartz per hour

8f + 14b = 51 f/h

13f + 6b = 41 f/h

51/41 = 1.2439

multiply 13f and 6b by this number so that both sides equal 51 f/h and you can set them equal to each other:

8f + 14b = 51 f/h

16.1707f + 7.463b = 51 f/h

thus:

(8f + 14b) = (16.1707f + 7.463b)

subtract 8f and 14b from both sides

0 = 8.1707f - 6.537b

add 6.537b to both sides

6.537b = 8.1707f

multiply by a thousand for simplicity

6537b =approx= 8171f

add them together: 14708 total

divide by 51 to get 288.392

so now divide 6537 by 288.392 = 22.667 f/h for Bars

divide 8171 by 288.392 = 28.333 f/h for Foos

Am I even close? lol

You're not even close. Substitute your answers into the original questions, and you will easily see that they are incorrect. Bloody extravagent answer, though.

8f + 14b = 51 F/hr.

13f + 6b = 41 F/hr.

Multiply the second equation by (-7/3) to get two equations with two variables that will cancel one variable when added together.

-7/3(13f + 6b = 41 F/hr.) ->

(-91/3)f - 14b = (-287/3) F/hr.

Now add this to the first equation:

(-91/3)f - 14b = (-287/3) F/hr.

+ 8f + 14b = 51 F/hr. ->

(-67/3)f = (-134/3) F/hr. ->

f = 2 F/hr.

Substitute f = 2 into the either original equation.

8(2) + 14b = 51 F/hr.

16 + 14b = 51 F/hr.

14b = 35 F/hr.

b = (5/2) F/hr. = 2.5 F/hr.

Plug these rates into the original equations to check.

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