math: word problem..help pls..?

Question

You are organizing a three-day back-country ski trip to Roger’s Pass for students in an outdoor club at St. Mary's College. You have approached two local busing companies for group cost information. The companies have presented you with their cost proposals for round-trip group travel:

Company A: $55 per person for a group of up to 40 students

Company B: $60 per person for a group of up to 25 students, with a discounted rate of $45 per person for each additional person in larger group size of between 25 and 40.

Let x denote the number of students who are considering participating in this trip. Let the function A(x) represent the total cost of the trip with company A and let B(x) represent the total cost of the trip with company B.

a)Determine the algebraic formulas for A(x) and B(x) for a domain of [0, 40].

b)For what value of x (number of students traveling) is the total cost the same for both companies?

Answer 1

A(x) = 55x. That's the easy part.
B(x) = 60x if x is in [0,25]. If x is in [25,40], B(x) = 60*25 + 45(x -25), which may be more conveniently written is 375 + 45x.

Setting A(x) = B(x) and solving, you get 37 1/2 students.

Assuming I didn't make an error -- and further assuming that your teacher has a morbid sense of humor -- the answer is there is no such x, unless part of the trip involves a reenactment of the Texas Chainsaw Massacre

(That said, the notation [0,40] assumes x is a continuous variable, notwithstanding that given the conditions of the problem it clearly has to be integer-valued.]

Answer 2

i visit coach you the thank you to set those up, yet you're waiting to do the artwork your self.... For the 1st concern, you already know that D + Q = 27. this skill that D = 27 -Q, and Q = 27 -D. you to boot to might desire to appreciate that 10D + 25Q = 510, by actuality dimes are 10 cents and quarters are 25 cents. So 10 x considered one of those dimes, plus 25 x considered one of those quarters, is 510 cents. incredibly of D, you will possibly be able to desire to apply 27 - Q, precise? by actuality which you already know from the 1st step that considered one of those dimes is resembling 27 minus considered one of those quarters. So replace that throughout. 10 (27-Q) + 25Q = 510 treatment for Q. Your answer might desire to be under 27 (there are in fact 27 money finished) and it is going to be a great form (or the respond might desire to hold forth 5, no longer 0). xxxxxxxxxxxx the subsequent one, set up an identical way. C + A = 220. considered one of those teenagers plus adults is 220. So, 220 - C =A. And 220 - A = C. you to boot to might desire to appreciate that a million.5C + 4A = 630 a million.5 money situations considered one of those teenagers, plus 4 money situations considered one of those adults, is 630. So do a substitution. incredibly of A, why no longer use (220 - C)? a million.5C + 4(220-C) = 630 treatment for C.