Question

A leaky pool loses 2 1/4 inches of water each day. Jermaine and Mildred are asked to determine the change in the amount of water in the pool over 5 days.

Jermaine’s Solution Mildred’s Solution

5(-2 1/4) 5(-2 1/4)
5(-2 -1/4) 5(-2 -1/4)
-10 -1/4 -10 -5/4
-10 1/4 -11 1/4

Which describes the reasoning used to determine whose solution is correct?

A. Jermaine is correct because -10 -1/4 equals -10 1/4.
B.Jermaine is correct because he distributed 5 correctly.
C.Mildred is correct because she multiplied 5 by –2 but not by -1/4.
D.Mildred is correct because she distributed 5 correctly.

Answer 1

Mildred's solution is correct.

5(-2 1/4) = 5(-2 + -1/4) = 5(-2) + 5(-1/4) = -10 + -5/4 = -10 + -1 1/4 = -11 1/4

Answer 2

Answer: D. Mildred is correct because she distributed 5 correctly.

Explanation:

Since, the loss of water in one day =
`2(1)/(4)\text{ inches}`

⇒ The loss of water in 5 days =
`5(2(1)/(4))\text{ inches}`

⇒ The loss can be written with negative sign,

Thus, the expression that shows the changes in quantity of water in 5 days,

`-5(2(1)/(4))`

`=-5(2+(1)/(4))`

`=5(-2-(1)/(4))`

`=-10-(5)/(4)`

`=-10-1(1)/(4)`

`=-10-1-(1)/(4)`

`=-11-(1)/(4)`

`=-11(1)/(4)`

Since, the above steps are similar to that of Mildred's solution,

⇒ Mildred is correct.

Also, By the above explanation it is clear that jermaine incorrectly distribute 5 in his third steps.

⇒ Option D is correct.