IRA Rollover

Archive for February, 2007

Question: College algebra word problems, Please Help?

College Algebra: Word problem dealing with linear equations.

1) Rollowheel, Inc. can manufacture a pair of in-line skates for $43.53. Daily fixed costs of manufacturing in-line skates amount to $742.72. A pair of in-line skates can be sold for $89.95. Find equations expressing the expenses “E” and the revenue “R” as functions of x, the number of pairs manufactured and sold. At what production level will expenses equal revenues?

2) For it’s sales staff, a company offers two salary options. One is $326 per wk. plus commission of 31/2% of sales. The other is $200. per wk. plus 41/4% of sales. Find equations that express incomes as functions of sales, and find the weekly sales level that produces equal salaries?

3) A woman invested a $22,000 rollover IRA account in three banks paying 5%, 6%, and 7% annual interest. She invested $2,000 more at 6% than at 5%. The total annual interest she earned was $1,370. How much did she invest at each rate.

Please Help!!!!

Answer: << Rollowheel, Inc. can manufacture a pair of in-line skates for $43.53. Daily fixed costs of manufacturing in-line skates amount to $742.72. A pair of in-line skates can be sold for $89.95. Find equations expressing the expenses “E” and the revenue “R” as functions of x, the number of pairs manufactured and sold. At what production level will expenses equal revenues? >>

Let

x = number of pairs of in-line skates

Expense = E = 742.72 + 43.53x

Revenue = R = 89.95x

For Expense to be equal to Revenue,

742.72 + 43.53x = 89.95x

Solving for “x”,

89.95x – 43.53x = 742.72

x = 742.72/46.32

x = 16 pairs (for revenue to be equal to expenses)

<< For it's sales staff, a company offers two salary options. One is $326 per wk. plus commission of 31/2% of sales. The other is $200. per wk. plus 41/4% of sales. Find equations that express incomes as functions of sales, and find the weekly sales level that produces equal salaries? >>

Option 1: S = 326 + 0.035x

Option 2: S = 200 + 0.0425x

where

S = weekly salary
x = amount of sales

For Option 1 to be equal to Option 2,

326 + 0.035x = 200 + 0.0425x

Combining like terms,

0.0425x – 0.035x = 326 – 200

0.0075x = 126

x = 16,800

<< A woman invested a $22,000 rollover IRA account in three banks paying 5%, 6%, and 7% annual interest. She invested $2,000 more at 6% than at 5%. The total annual interest she earned was $1,370. How much did she invest at each rate. >>

Let

x = amount invested at 5%
y = amount invested at 6%
z = amount invested at 7%

Your working equations are:

Equation 1: x + y + z = 22000

Equation 2: y = x + 2000

Equation 3: 0.05x + 0.06y + 0.07z = 1370

You have three equations in 3 unknowns. I will let you do the required algebraic procedure to determine the respective values of “x”, “y” and “z”.

Good luck.

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