The rates charged by a local delivery service consist of a fixed cost, F, and a

Question

The rates charged by a local delivery service consist of a fixed cost, F, and a variable rate, r, based on the weight, W, of the package being delivered. Total cost, C, to the customer is determined by the following formula: C = F + rW. If it costs $10.10 to deliver a 12-lb package and $13.95 to deliver a 19-lb package, find fixed rate, F, and the cost per pound, r. Write two simultaneous equations and solve using Determinant method A contractor purchases 350 pieces of 2 times 4 lumber and 200 pieces of 2 times 6 lumber at a total cost of $1077.50 Several days later he buys another 140 of the 2 times 4s, and 125 more of the 2 times 6s for a total of $527.75. What is the cost of a 2 times 4? Of a 2 times 6? Write two simultaneous equations and solve using determinant method

Explanation / Answer

1.46 Let the fixed cost charged by the delivery service be $ x and let the variable rate be $ y per lb.

Then, as per the given formula, we have x + 12y = 10.10 and x + 19y = 13.95. Then, using the method of determinants ( Cramer’s rule), we have D = I 1   12 I = (19-12) = 7.

I 1 19 I

Also, Dx = I 10.10   12 I = (19*10.10-12*13.95) =191.90- 174.40 = 24.50;

I 13.95 19 I

and Dy = I 1   10.10 I = (13.95 -10.10) = 3.85

I 1   13.95 I

Therefore, x = Dx /D = 24.50/7 = 3.50 and y = Dy /D = 3.85/7 = 0.55.

Thus, the Fixed rate F is $ 3.50 and the variable rate is $ 0.55 per lb.

1.47. Let the costs of 1 piece of 2x4 lumber and 2x6 lumber be $ x and $ y respectively. Then, we have 350x + 200y = 1077.50 and 140x +125y = 527.75.

Then, using the method of determinants, we have D = I 350 200 I = (43750-28000) = 15750.

I 140 125 I

Also, Dx = I 1077.50   200 I = (134687.50- 105550) =29137.50

I 527.75   125 I

and Dy = I 350   1077.50 I = (184712.50 -150850 ) = 33862.50

I 140     527.75 I

Therefore, x = Dx /D = 29137.50/15750 = 1.85 and y = Dy /D = 33862.50 /15750 = 2.15.

Thus, the costs of 1 piece of 2x4 lumber and 2x6 lumber are $1.85 and $ 2.15 respectively.

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