Question

the data in the following table can be used to predict the number of drinks required for a person of a specified weight to be considered legally intoxicated. use the data in the table to draw a graph and to estimate the number of drinks that a 140-lb person would consume in order to be considered intoxicated. then predict the number of drinks a 240-lb person would consume in order to be considered intoxicated. (the small-sized drink of any alcoholic beverage is considered to be one drink.)
input, body weight (in pounds)
120
160
180
220
output, number of drinks
3
4
4.5
5.5
a 140-lb person can consume 3.5 drink(s) in order to be considered intoxicated (type an integer or a decimal)
a 240-lb person can consume drink(s) in order to be considered intoxicated (type an integer or a decimal)

Explanation:

Step1: Identify the relationship

We can observe the data: when weight is 120 lb, drinks = 3; 160 lb, drinks = 4; 180 lb, drinks = 4.5; 220 lb, drinks = 5.5. Let's assume a linear relationship between weight (x) and number of drinks (y). The general form of a linear equation is \( y = mx + b \).

Step2: Calculate the slope (m)

Using two points, say (120, 3) and (220, 5.5). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5.5 - 3}{220 - 120}=\frac{2.5}{100}=0.025 \).

Step3: Find the y-intercept (b)

Using point (120, 3) in \( y = mx + b \): \( 3 = 0.025\times120 + b \). \( 3 = 3 + b \), so \( b = 0 \). Wait, that seems off. Wait, maybe the relationship is inverse? Wait, actually, the number of drinks should be proportional to weight? Wait, no, maybe the correct relationship is that the number of drinks (y) and weight (x) have a linear relationship. Wait, let's check the ratio. For 120 lb: 3 drinks, so per 40 lb, 1 drink (120/3=40, 160/4=40, 180/4.5=40, 220/5.5=40). Ah! So the relationship is \( x = 40y \), so \( y=\frac{x}{40} \).

Step4: Calculate for 240 lb

Using \( y=\frac{x}{40} \), for x=240, \( y=\frac{240}{40}=6 \). Wait, but wait, the first part: a 140-lb person can consume 3.5 drinks. Let's check with \( y=\frac{x}{40} \), 140/40=3.5. Yes! So the formula is \( y = \frac{\text{weight}}{40} \).

Step5: Verify for 140 lb

\( \frac{140}{40}=3.5 \), which matches. For 240 lb: \( \frac{240}{40}=6 \).

Answer:

For a 140-lb person: 3.5 (already given, but the calculation confirms). For a 240-lb person: 6.

Wait, the question has two parts: "A 140-lb person can consume 3.5 drink(s) in order to be considered intoxicated" (which is given, but we verified with the formula \( y = \frac{x}{40} \), 140/40=3.5). Then "A 240-lb person can consume \(\boxed{6}\) drink(s) in order to be considered intoxicated" (using \( 240/40 = 6 \)).