Question

alberto and rebecca toss horseshoes at a stake. whoevers horseshoe is closer to the stake wins a point.

1. reasoning what integer best describes the location of albertos horseshoe in relation to the stake? what integer best describes the location of rebeccas horseshoe?
2. critique reasoning alberto says that - 3 is less than 2, so he wins a point. is alberto correct? explain.
3. model with math find the distance from albertos horseshoe to rebeccas horseshoe. explain.

Explanation:

Step1: Analyze positive and negative integer meaning

Positive integers mean past the stake and negative integers mean before the stake. Alberto's horseshoe is - 3 feet (3 feet in front of the stake), so the integer representing its location is - 3. Rebecca's horseshoe is 2 feet past the stake, so the integer representing its location is 2.

Step2: Compare the absolute - values

The absolute - value of - 3 is |-3|=3, and the absolute - value of 2 is |2| = 2. Since 2<3, Rebecca's horseshoe is closer to the stake. Alberto is incorrect.

Step3: Calculate the distance between the horseshoes

To find the distance between Alberto's and Rebecca's horseshoes, we use the formula for the distance between two numbers on the number line: d=|a - b|. Here, a=-3 and b = 2. So d=| - 3-2|=| - 5|=5 or d=|2-( - 3)|=|2 + 3|=5.

Answer:

Alberto is incorrect. Rebecca's horseshoe is closer to the stake because |-3| = 3 and |2|=2, and 2 < 3. The distance from Alberto's horseshoe to Rebecca's horseshoe is 5 feet.