*PLEASE HELP ME ASAP I WANT TO CRY THIS IS SO HARD :((* Rollowheel, Inc., can manufac-
ture 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 num-
ber 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".