Question

A weightlifter is using a weightlifting bar that weighs 45 pounds. If x represents the amount of weight that the weightlifter puts on the bar and y represents the total amount that the weightlifter lifts, with the weight of the bar included, which of these functions models this situation, and why?

1) y = 45 + x
2) y = 45 - x
3) y = 45 * x
4) y = 45 / x

Answer 1

The function y = 45 + x accurately represents the situation where a weightlifter is lifting a bar with additional weight because it directly adds the weight placed on the bar to the bar's weight.

Step-by-step explanation:

The proper function that models the situation where a weightlifter is lifting a weightlifting bar along with the additional weights is y = 45 + x. Here, x represents the amount of weight added to the 45-pound bar (the weight of the bar itself), and y represents the total weight being lifted. This relationship is direct and additive because every pound of weight added to the bar increases the total weight by that same amount. Therefore, the correct model for this real-world problem is a linear equation with a slope of 1 and a y-intercept of 45, where the total weight lifted y increases by 1 pound for each additional pound x added to the bar. The function that models this situation is y = 45 + x.

Since the weightlifter is using a weightlifting bar that weighs 45 pounds, we start with a base weight of 45. The weightlifter then adds additional weight to the bar, which is represented by x. The total weight lifted, including the weight of the bar, is given by y. So, we add x to the base weight of 45 to get the total weight lifted. Therefore, the function is y = 45 + x.