Write a linear equation to fit each situation.
1) A medical laboratory charges $30 for a consultation and an additional $10 per test. (Let t = the # of test, f(t) = the total fee.)
Answer: f(t)=30+10t
2) A 150 kg man goes on a diet and loses 1.4 kg/week. Relate weight to the number of weeks on the diet. (Identify variables as in #1.)
Answer: f(w)=150-1.4w, w=week, f(w)=total weight
3) 2 hours into a trip by car is 600 miles from its desitnation, Chicago. The car travels at an average speed of 50 mph. (Let t = time in hours, d(t) = distance from Chicago)
d(t)=600-50t
Are my answers correct? If not please help me.
For #3 wouldn't it be t-2 or something because it is 2 hours into trip
How would you incorporate that into the equation?
Your answers are almost correct! Just a small correction is needed in the third equation.
1) The equation you provided is correct: f(t) = 30 + 10t. This equation represents the total fee charged by the medical laboratory where t represents the number of tests conducted.
2) The equation you provided is also correct: f(w) = 150 - 1.4w. This equation represents the weight of a man on a diet where w represents the number of weeks he has been on the diet.
3) However, the equation for the car's distance from Chicago needs a small correction. Since the car is traveling away from Chicago, the equation should be: d(t) = 600 + 50t. This equation represents the distance from Chicago (d) based on the time in hours (t) and an average speed of 50 mph.
So, the corrected equation for situation 3 is: d(t) = 600 + 50t.
Overall, great job!