The total change in the water level of a lake from rhe beginning of April to the end if August was -4.7 inches. The table shows in the change in the water level from the beginning to the end of several months. Complete the table to show possible changes in the water level, in inches, fir July and August.
To find the possible changes in the water level for July and August, we need to subtract the changes in the water level for the previous months from the total change in water level.
Given that the total change in water level from April to August is -4.7 inches, and we have the changes for April, May, June, we can complete the table as follows:
```
Month Change in Water Level (in inches)
--------------------------------------------
April ?
May 1.9
June -2.3
July ?
August ?
```
To find the change in water level for April, we subtract the sum of changes in May, June, July, and August from the total change in water level:
April = -4.7 - 1.9 - (-2.3) - ? = -4.7 - 1.9 + 2.3 + ?
Since we know that the total change in water level from April to August is -4.7 inches, we can substitute this value back into the equation:
-4.7 = -4.7 - 1.9 + 2.3 + ?
Simplifying this equation, we get:
-4.7 = -4.7 - 1.9 + 2.3 + ? -> -4.7 = -4.3 + ?
To solve for ?, we subtract -4.3 from both sides:
? = -4.7 - (-4.3)
? = -4.7 + 4.3
? = -0.4
Therefore, the change in water level for April is -0.4 inches.
Now we can find the changes in water level for July and August by subtracting the accumulated changes from the total change in water level:
July = -4.7 - 1.9 - (-2.3) - (-0.4)
July = -4.7 - 1.9 + 2.3 + 0.4
Simplifying this equation, we get:
July = -4.7 - 1.9 + 2.3 + 0.4
July = -3.2
Therefore, the change in water level for July is -3.2 inches.
Finally, we can find the change in water level for August by subtracting the changes in April, May, June, and July from the total change in water level:
August = -4.7 - 1.9 - (-2.3) - (-0.4) - (-3.2)
August = -4.7 - 1.9 + 2.3 + 0.4 + 3.2
Simplifying this equation, we get:
August = -4.7 - 1.9 + 2.3 + 0.4 + 3.2
August = -1.7
Therefore, the change in water level for August is -1.7 inches.
Completing the table, we have:
```
Month Change in Water Level (in inches)
--------------------------------------------
April -0.4
May 1.9
June -2.3
July -3.2
August -1.7
```