system of linear equations in two unknowns by determinants

John Wu · 2006-09-04 05:31:42

hi, can any kind person help me out this 2 word problems??? thanks in advance

Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. all numbers are accurate to at least two significant digits.

(A) A shipment of 320 cell phones and radar detectors was destroyed due to a truck accident. on the insurance claim, the shipper stated that each phone was worth $110, each detector was worth $160, and their total value was $40700. how many of each were in the shipment?

(B)A machinery sales representative receives a fixed salary plus a sales commission each month. if $6200 is earned on sales of $70000 in one month and $4700 is earned on sales of $45000 in the following month, what are the fiexed salary and the commission percent?

Last edited by John Wu (2006-09-04 05:53:04)

mikau · 2006-09-04 12:22:37

The first is easy, and like most coin problems.

There were 320 cell phones AND radar dectectors in all. So

c + d = 320

the total cost of these items will be 110 for every cell phone and 160 for each radar detector. The total cost is 40700 so
110c + 160d = 40700
that gives you two equations. I hope you know how to solve with determinants because I haven't used matrices in a long time.

The second I'm a little unsure about because I'm not entirley sure what a sales commision is. But it looks like the money the represenative earns (lets call this y) is a certain percetage (m), of the sales (x) plus his monlthy salary (b)
so y = mx + b

pluging in the sales values for x and the profit values for y gives us:

6200 = 70000m + b
4700 = 45000m + b

and again use matrices to solve. The fixed salary would be b and the comision rate is m.

John Wu · 2006-09-04 19:32:17

i have to answer $2000, but how to i calculate to get the percent??

mikau · 2006-09-06 14:45:10

2000 would be "b" the monthly pay which is a constant. The percentage is m. You can use either equation:

6200 = 70000m + b
4700 = 45000m + b

replace b with 2000 and solve.

Math Is Fun Forum

#1 2006-09-04 05:31:42

system of linear equations in two unknowns by determinants

#2 2006-09-04 12:22:37

Re: system of linear equations in two unknowns by determinants

#3 2006-09-04 19:32:17

Re: system of linear equations in two unknowns by determinants

#4 2006-09-06 14:45:10

Re: system of linear equations in two unknowns by determinants

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