# _____
Name: ______
Math 11a -- Spring 2000
Final – Part II
Instructions: Put you name and number at the top of the page in the blanks provided. Show all of your work clearly. You may use the back of the page to show extra work, as long as you label it clearly. This is a test of algebra skills, and therefore all word problems will receive no credit unless there is an algebra equation, which yields the correct answer, and the equation is backed by defined variables for all unknowns! You may use a calculator. Good luck!
New Material Continued
28. The following must be solved using 2 equations and 2 unknowns. A riverboat can
head 340 miles upriver in 19 hours but the return trip takes only 14 hours. Find the
the speed of the ship in still water to the nearest tenth of a mph. (Use decimals for
the final answer, and not fractions.)
29. You must use 2 equations and 2 unknowns to solve the following. The Deli charges
$3.80 for a breakfast of 3 eggs and 4 strips of bacon. The charge is $2.75 for 2 eggs
and 3 strips of bacon. Find the cost of each egg and each strip of bacon. Don’t
solve this problem, just set up the system that could be used to solve it.
For 30, 31 & 32 the answers must be given as ordered pairs if there is a single solution.
30. You must use the method of elimination to solve the following system of equations.
8x = 3y 2
4/7 x y = -5/2
31. You must use the method of substitution to solve the following system of equations.
4y = 2x 3
x 2y = 4
32. You must use the graphing method to solve the following system of equations.
(Show your work here and graph on the graph paper on the next page.)
2x + y = -5
3y = -x
Review Material
33. For the equation:x 3y = 12
a)Put the equation in slope-intercept form
b)Give the y-intercept as an ordered pair
c)Give the x-intercept as an ordered pair
d)State the slope. m =
e) Give an equation of a line perpendicular to the given line.
f) Give an equation of a line parallel to the given line.
34. Graph the following linear inequality in 2 variables on the next page. Show the work
for obtaining the 3 points to graph the boundary line, and show the work for your 2
check points.2x 3y < 6
35. Express the sum of 3 consecutive even integers as an unsimplified expression.
Define each integer!
36. A pay phone is holding its maximum number of 500 coins consisting of nickels,
dimes and quarters. The number of quarters is twice the number of dimes. If the
value of all the coins is $88.00, how many nickels are in the phone? Do not solve
this word problem, simply set up the problem using 1 equation and one unknown, so
that the answer could be found.
37. A $50,000 retirement pension is to be invested into two accounts: a money market
fund that pays 8.5% and a certificate of deposit that pays 10.5%. How much should
be invested at each rate in order to provide a yearly interest income of $4,550? Do
not solve, just set up the system or the one equation that would be used to solve.
38. Factor3a2 + 9ab + 3b2 + ab
39. Solve using factoring18x3 60x2 + 50x = 0
40. Solve 2 1 = -1
x + 1 x 2 2
41. Solve 4 = 2
y 3 y 3
42. Simplify 2x 5 4
6x + 9 2x2 + 3x
43. It takes pipe A 20 days to fill a fish pond. Pipe B takes 15 days. Find how long it
takes both pipes together to fill the pond. Don’t solve the equation. Use one variable
and set up the equation that would be used to solve the problem.
44. Use long division to solve: -10x2 x3 21x + 18
x 6
45. A chemist working on his doctoral degree a MIT needs 12 liters of a 50% acid
solution for a lab experiment. The stockroom only has 40% and 70% solutions.
How much of each solution should be mixed together to form 12 liters of a 50%
solution?