Question

A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply.
x = one-half y minus 3
2 x minus y = negative 6
2 x minus y = negative 3
x = one-half (y minus 3)
y = 10 (x minus 1)

Answer 1

To model the situation with the given descriptions, we need to translate the statements into mathematical equations.

1. "A smaller number is 3 less than half a larger number."
This can be expressed as:
\[
x = \frac{1}{2}y - 3
\]

2. "The larger number is 10 times 1 less than the smaller number."
This translates to:
\[
y = 10(x - 1)
\]

Now let's check the equations that you provided to see which ones correspond to these statements:

1. \( x = \frac{1}{2}y - 3 \) - **This is correct.**

2. \( 2x - y = -6 \) - This is not equivalent to either of our derived equations from the problem.

3. \( 2x - y = -3 \) - This is not equivalent to either of our derived equations from the problem.

4. \( x = \frac{1}{2}(y - 3) \) - This does not match our description directly, as it implies a different relationship.

5. \( y = 10(x - 1) \) - **This is correct.**

Thus, the equations that can be used to model the situation are:
- \( x = \frac{1}{2}y - 3 \)
- \( y = 10(x - 1) \)