The river rose 4 feet above flood stage last night. If a= the river’s height at flood stage, b= the river’s height now (the morning after), which equations below say the same thing as the statement? Explain your choices by translating the equations into English and comparing the meaning with the original statement.

(a) a+b=4
(b) b-4=a
(c) a-4=b
(d) a+4=b
(e) b+4=b
(f) b-a=4

Not going to answer this, but going to give you something to think about how to answer it.

When you use the "+" sign, you are adding to something ... or putting more in.

When you use the "-" sign, you are taking away.

So, overnight, was water added or taken away from the river?

See if that helps narrow down the answer.

Matt

That does not help me much because I have no idea how to translate this problem into English. Please help me!

Here are all the possibilities translated into English:

Answer a: The height of flood stage plus the height right now equals 4 feet.

Answer b: The height right now minus 4 feet equals the height of the water at flood stage.

Answer c: The height of the water at flood stage minus 4 feet is the height of the water now.

Answer d: The height of the water at flood stage plus 4 feet equals how much water there is now.

e: The height now plus 4 feet is the height now.

f: The height now minus the height at flood stage equals 4 feet.

To determine which equation(s) say the same thing as the original statement, we need to analyze the meaning and compare it with the given equations.

The original statement says that the river rose 4 feet above flood stage last night. This means that the current height of the river (b) is 4 feet higher than the height at flood stage (a).

Now let's analyze the equations one by one:

(a) a + b = 4: This equation states that the sum of the height at flood stage and the current height is equal to 4. This does not accurately represent the statement because it does not account for the fact that the river rose up by 4 feet.

(b) b - 4 = a: This equation states that the current height minus 4 feet is equal to the height at flood stage. This accurately represents the statement because the river rose by 4 feet, so the height at flood stage (a) must be 4 feet below the current height (b).

(c) a - 4 = b: This equation states that the height at flood stage minus 4 feet is equal to the current height. This does not accurately represent the statement because it implies that the current height is 4 feet below the height at flood stage, which is the opposite of what happened.

(d) a + 4 = b: This equation states that the height at flood stage plus 4 feet is equal to the current height. This accurately represents the statement because the river rose by 4 feet, so the current height (b) must be 4 feet higher than the height at flood stage (a).

(e) b + 4 = b: This equation states that the current height plus 4 feet is equal to the current height. This does not accurately represent the statement because it implies that the current height is unchanged, which is not the case.

(f) b - a = 4: This equation states that the current height minus the height at flood stage is equal to 4. This does not accurately represent the statement because it does not account for the fact that the river rose up by 4 feet.

Based on this analysis, the equations that say the same thing as the original statement are equations (b) and (d), where (b) represents the relationship between the current height (b) and the height at flood stage (a).