 3.2.1: If computers sell for $1180 per unit and hard drives sell for $125 ...
 3.2.2: The combined yearly interest for x dollars invested at 12% and y do...
 3.2.3: The total amount of acid in x milliliters of a 9% acid solution and...
 3.2.4: If x represents the average rate of a plane in still air and y repr...
 3.2.5: If x + y represents a motorboats rate with the current, in miles pe...
 3.2.6: A companys ______________ function is the money generated by sellin...
 3.2.7: A company has a graph that shows the money it generates by selling ...
 3.2.8: C(x) = 1.2x + 1500 R(x) = 1.7x
 3.2.9: At some point, its time to kick, or gently ease, kids off the paren...
 3.2.10: As sequels to horror films increase, so does the body count. Wes Cr...
 3.2.11: One week a computer store sold a total of 36 computers and external...
 3.2.12: There were 180 people at a civic club fundraiser. Members paid $4.5...
 3.2.13: You invested $7000 in two accounts paying 6% and 8% annual interest...
 3.2.14: You invested $11,000 in stocks and bonds, paying 5% and 8% annual i...
 3.2.15: You invested money in two funds. Last year, the first fund paid a d...
 3.2.16: You invested money in two funds. Last year, the first fund paid a d...
 3.2.17: Things did not go quite as planned. You invested $20,000, part of i...
 3.2.18: Things did not go quite as planned. You invested $30,000, part of i...
 3.2.19: A wine company needs to blend a California wine with a 5% alcohol c...
 3.2.20: A jeweler needs to mix an alloy with a 16% gold content and an allo...
 3.2.21: For thousands of years, gold has been considered one of Earths most...
 3.2.22: In the Peanuts cartoon shown, solve the problem that is sending Pep...
 3.2.23: The manager of a candystand at a large multiplex cinema has a popul...
 3.2.24: A grocer needs to mix raisins at $2.00 per pound with granola at $3...
 3.2.25: A coin purse contains a mixture of 15 coins in nickels and dimes. T...
 3.2.26: A coin purse contains a mixture of 15 coins in dimes and quarters. ...
 3.2.27: When a small plane flies with the wind, it can travel 800 miles in ...
 3.2.28: When a plane flies with the wind, it can travel 4200 miles in 6 hou...
 3.2.29: A boats crew rowed 16 kilometers downstream, with the current, in 2...
 3.2.30: A motorboat traveled 36 miles downstream, with the current, in 1.5 ...
 3.2.31: With the current, you can canoe 24 miles in 4 hours. Against the sa...
 3.2.32: With the current, you can row 24 miles in 3 hours. Against the same...
 3.2.33: A student has two test scores. The difference between the scores is...
 3.2.34: A student has two test scores. The difference between the scores is...
 3.2.35: In Exercises 3536, an isosceles triangle containing two angles with...
 3.2.36: In Exercises 3536, an isosceles triangle containing two angles with...
 3.2.37: A rectangular lot whose perimeter is 220 feet is fenced along three...
 3.2.38: A rectangular lot whose perimeter is 260 feet is fenced along three...
 3.2.39: A new restaurant is to contain twoseat tables and fourseat tables...
 3.2.40: A hotel has 200 rooms. Those with kitchen facilities rent for $100 ...
 3.2.41: How many radios must be produced and sold for the company to break ...
 3.2.42: More than how many radios must be produced and sold for the company...
 3.2.43: Use the formulas shown in the voice balloons to find R(200)  C(200...
 3.2.44: Use the formulas shown in the voice balloons to find R(300)  C(300...
 3.2.45: a. Use the formulas shown in the voice balloons to write the compan...
 3.2.46: a. Use the formulas shown in the voice balloons to write the compan...
 3.2.47: A company that manufactures small canoes has a fixed cost of $18,00...
 3.2.48: A company that manufactures bicycles has a fixed cost of $100,000. ...
 3.2.49: You invest in a new play. The cost includes an overhead of $30,000,...
 3.2.50: You invested $30,000 and started a business writing greeting cards....
 3.2.51: Describe the conditions in a problem that enable it to be solved us...
 3.2.52: Write a word problem that can be solved by translating to a system ...
 3.2.53: Describe a revenue function for a business venture.
 3.2.54: Describe a cost function for a business venture. What are the two k...
 3.2.55: What is the profit function for a business venture and how is it de...
 3.2.56: Describe the breakeven point for a business.
 3.2.57: The law of supply and demand states that, in a free market economy,...
 3.2.58: Many students hate mixture problems and decide to ignore them, stat...
 3.2.59: R(x) = 50x, C(x) = 20x + 180
 3.2.60: R(x) = 92.5x, C(x) = 52x + 1782
 3.2.61: Use the procedure in Exercises 5960 to verify your work for any one...
 3.2.62: A system of linear equations can be used to model and compare the f...
 3.2.63: I should mix 6 liters of a 50% acid solution with 4 liters of a 25%...
 3.2.64: If I know the perimeter of this rectangle and triangle, each in the...
 3.2.65: You told me that you flew against the wind from Miami to Seattle, 2...
 3.2.66: The radiator in your car contains 4 gallons of antifreeze and water...
 3.2.67: A marching band has 52 members, and there are 24 in the pompom squ...
 3.2.68: A boy has as many brothers as he has sisters. Each of his sisters h...
 3.2.69: When entering your test score into a computer, your professor accid...
 3.2.70: A dealer paid a total of $67 for mangos and avocados. The mangos we...
 3.2.71: Passing through (2, 5) and (6, 13) (Section 2.5, Example 2)
 3.2.72: Passing through (3, 0) and parallel to the line whose equation is ...
 3.2.73: Find the domain of g(x) = x  2 3  x . (Section 2.3, Example 1)
 3.2.74: If x = 3, y = 2, and z = 3, does the ordered triple (x, y, z) sati...
 3.2.75: Consider the following equations: 5x  2y  4z = 3 Equation 1 3x + ...
 3.2.76: Write an equation involving a, b, and c based on the following desc...
Solutions for Chapter 3.2: Problem Solving and Business Applications Using Systems of Equations
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 3.2: Problem Solving and Business Applications Using Systems of Equations
Get Full SolutionsChapter 3.2: Problem Solving and Business Applications Using Systems of Equations includes 76 full stepbystep solutions. Since 76 problems in chapter 3.2: Problem Solving and Business Applications Using Systems of Equations have been answered, more than 52775 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Column space C (A) =
space of all combinations of the columns of A.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Iterative method.
A sequence of steps intended to approach the desired solution.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.