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Grandma is removing weeds from her garden. She estimates that there are 250 weeds in the garden at the moment, and she can remove weeds at a rate of 5 per minute. At this rate, how many minutes will it take her to only have 30 weeds remaining in the garden?

Equation: ___________________

options:

A. 250 + 5m = 30

B. 30 - 5m = 250

C. 5m - 250 = 30

D. 250 - 5m =30

3 answers

To find the equation that represents the situation, we start with the current number of weeds, which is 250. Grandma will be removing weeds at a rate of 5 per minute, so after \( m \) minutes, the number of weeds removed would be \( 5m \).

We want to know how long it will take for the number of weeds to go from 250 to 30. This gives us the equation:

\[ 250 - 5m = 30 \]

So, the correct choice is:

D. 250 - 5m = 30

The Celsius to Fahrenheit formula: F = 9 over 5C + 32

Solve this formula for C. Check all answers that are true.

options:

A). First step is to multiply by 9 on each side.

B). First step is to add 32 to both sides.

C). The next step from F - 32 = 9/5 C, could be to multiply both sides by 5

D). The next step from F - 32 = 9/5 C, could be to divide both sides by 5

E). Solution: 5/9F - 32 = C

F). To solve this equation for C, you would have to distribute at some point.

Let's solve the equation \( F = \frac{9}{5}C + 32 \) for \( C \) step by step:

  1. First step: To isolate the term with \( C \), subtract 32 from both sides. \[ F - 32 = \frac{9}{5}C \]

    • This means that option B ("First step is to add 32 to both sides") is false, as it should be subtraction.

  2. Next steps: Now we can rearrange \( F - 32 = \frac{9}{5}C \).

    • To get \( C \) by itself, we can multiply both sides by \( \frac{5}{9} \): \[ C = \frac{5}{9}(F - 32) \]

    • This shows that option C ("The next step from F - 32 = 9/5 C, could be to multiply both sides by 5") is false, since we would actually multiply by \( \frac{5}{9} \) if we were to isolate \( C \).

    • Option D ("The next step from F - 32 = 9/5 C, could be to divide both sides by 5") is also false, as dividing both sides by 5 wouldn't isolate \( C \) correctly; we need to divide by \( \frac{9}{5} \).

  3. The final solution we derived is: \[ C = \frac{5}{9}(F - 32) \]

    • This means that option E ("Solution: 5/9F - 32 = C") is false because the expression should be \( \frac{5}{9}(F - 32) \) instead of subtracting 32 from \( \frac{5}{9}F \).

  4. Option F ("To solve this equation for C, you would have to distribute at some point") is true because after multiplying \( \frac{5}{9} \) with \( (F - 32) \), you will indeed distribute the \( \frac{5}{9} \).

In summary:

  • True options: F
  • False options: A, B, C, D, E