Question

Match an equation to each of these situations. Be prepared to share your reasoning.

1. The water level in a reservoir is now 52 meters. If this
0.23x = 52
was a 23% increase, what was the initial depth?
0.77x = 52
1.23x = 52
1.77x = 52
2. The snow is now 52 inches deep. If this was a 77%
decrease, what was the initial depth?

Answer 1

To find the initial depth, we need to solve the equations 0.23x = 52 and 0.23x = 52 in two different situations - a 23% increase and a 77% decrease. The initial depth of the reservoir was approximately 226.087 meters, while the initial depth of the snow was approximately 226.087 inches.

Step-by-step explanation:

1. To find the initial depth of the reservoir, we need to determine the value of 'x' in the equation 0.23x = 52. Since 52 is the current water level and it represents a 23% increase, we can set up the equation as follows:

1. 0.23x = 52

Solving this equation by dividing both sides by 0.23, we get: x = 52 / 0.23 = 226.087 meters. Therefore, the initial depth of the reservoir was approximately 226.087 meters.

2. To find the initial depth of the snow, we need to determine the value of 'x' in the equation 0.23x = 52. Since 52 is the current snow depth and it represents a 77% decrease, we can set up the equation as follows:

1. 0.23x = 52

Solving this equation by dividing both sides by 0.23, we get: x = 52 / 0.23 = 226.087 inches. Therefore, the initial depth of the snow was approximately 226.087 inches.

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