Question

Need help with problem 40,41 and 42! 15 points

Answer 1

40) w = 32/3

41) x = 23/4

42) w = 1/12

Explanation:

40) Real world problem:

If Lisa takes
`$ 7(3)/(8) $` of the pie from a total of
`$w$` slices, then the remaining pie is
`$ 3 (7)/(24) $`. Find w.

So, the equation would become:

`$ w - 7 (3)/(8) = 3 (7)/(24) $`

`$ \implies w = 3 (7)/(24) + 7 (3)/(8) $`

This can be written as:

`$ w = 3 + (7)/(24) + 7 + (3)/(8) $`

This is equivalent to
`$ 3 + (7)/(24) + 7 + (9)/(24) $`

Since, the denominator is the same, the numerators can be added now.

`$ \implies  w = 10 + (16)/(24) $`

`$ \implies w = 10 + (2)/(3) $`

`$ i.e., w = 10 (2)/(3) = (32)/(3) $`

Hence, the answer is 32/3.

41) The given equation is:
`$ 2 (1)/(2) + x = 8(1)/(4) $`

`$ 2 (1)/(2) = (5)/(2) $` and

`$ 8 (1)/(4) = (33)/(4) $`

So,
`$ x = (33)/(4) - (10)/(4) $`

`$ \implies x = (23)/(4) $`

The answer is 23/4.

42) The given equation is
`$ w - (1)/(3)  = (5)/(12)`

`$ \implies w = (5)/(12) - (1)/(3) $`

`$ w = (5)/(12) - (4)/(12) $`

`$ w = (1)/(12) $`

The answer is 1/12.