Question

A child's pool is filled to the top. On day 1, the level of the water in the pool decreases by
`1(1)/(3)` inches. On day 2, the level of the water decreases by
`(3)/(8)` inch. What number represents the total change in the water level after 2 days?

A.
`-1(17)/(24)` inches C.
`(23)/(24)` inch

B.
`(-23)/(24)` inch D.
`1(17)/(24)` inches

Answer 1

`( - 1 (17)/(24) \: inches)`

Explanation:

`1 (1)/(3) + (3)/(8) \\ = (4)/(3) + (3)/(8) \\ = (32)/(24) + (9)/(24) \\ = (41)/(24) = 1(17)/(24)`

Answer 2

`\displaystyle A) -1 (17)/(21)`

Explanation:

refer the attachment

the blue line refers the amount of reduction in the first day and the black line refers the amount of reduction in the second day

note that the total amount of depth of the the pool isn't specified therefore we can't assume the total depth of the pool to be 1 and as it says 'decrease' we are dealing with negative numbers

so

`\rm \displaystyle \text{the level of the water in the pool decreases by $1(1)/(3)$ inches} \iff \boxed{- 1(1)/(3) }`

likewise

`\rm \displaystyle \text{the level of the water in the pool decreases by $(3)/(8)$ inches} \iff \boxed{- (3)/(8) }`

since it wants the total amount of reduction we just need to add them which yields:

`\displaystyle - 1 (1)/(3) + \bigg(- (3)/(8)\bigg)`

simplify complex fraction:

`\displaystyle - (4)/(3) + \bigg(- (3)/(8) \bigg)`

simplify addition:

`\displaystyle - (41)/(21)`

the option is given in complex fraction thus convert it to complex fraction:

`\displaystyle -1 (17)/(21)`

and we're done!

hence our answer is A