Math 100A
Solving Linear Functions II
Name:
1. Let f (t) = 2t + 7. Does the equation have no solution, one solution, or an infinite number of
solutions?
(a) f (t) = 7
(b) f (t) = f (t + 1) − 2
(c) f (t) = f (−t)
(d) f (t) + 1 = f (t + 1)
2. Vandelay Industries offers three formulas for the weekly salary of its sales people, depending
on the number of sales, s, made each week:
(i) 100 + 0.10s dollars
(ii) 150 + 0.05s dollars
(iii) 175 dollars
(a) How many sales must be made under option (i) to receive $200/week?
(b) How many sales must be made under option (iii) to receive $200/week?
(c) At what sales level do options (i) and (ii) produce the same salary?
(d) At what sales level do options (ii) and (iii) produce the same salary?
Math 100A
Solving Linear Functions II
3. You have a coupon worth $20 off the purchase of a scientific calculator. At the same time, the
calculator is offered with a discount of 15%, and no further discounts apply.
(a) Write a function giving the discounted price p(x) as a function of the original price x in
the case of the $20 coupon.
(b) Write a function giving the discounted price p(x) as a function of the original price x in
the case of the 15% discount.
(c) For what original price on the calculator do you pay the same amount for each discount?
4. The floor plan for a room is shown in the figure. The total area is 144 ft2 . What is the missing
length? Note: the figure is not drawn to scale.
x
4
6
5. If a + mx = b + nx, what can be said about the constants a, b, m, and n if the equation has
(a) One solution?
(b) No solution?
(c) An infinite number of solutions?
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