alicia24
Answered

The cost, £C, of hiring a lorry to travel n miles is given by

C=a+bn

where a and b are constants.

The cost of travelling 100 miles is £82. the cost of travelling 250 miles is £157


a find out the value of a and b

b work out the cost of hiring a lorry to travel 300 miles


Please show working out clearly, ill award a brainliest answer!!!!!

Verified Answer :

nathan127

Part A:
C= a + bn

Make the two equations out of the words:
82 = a + b100 * 2.5     = 205 = a + b250
157 = a+ b250

Subtract the two,
205 = a + b250
- ( 157 = a + b250)
48 = a

Find b by substituting in a:
82 = a + b100
82 = 48 + b100
34 = b100
b = 0.34
Answer for part a: a = 48 , b = 0.34

Part B:
C = a +bn    <- when n = 300   , put in a and b, then solve
C = 48 + 0.34(300)
C = 48 + 102
C = 150

Cost when hiring a lorry to travel 300 miles is 150 pounds

Answer:

Part a) a = 32 and b = 0.5

Part b) £182 is the cost of hiring.

Step-by-step explanation:

Given expression is C = a + bn

where C is the cost of hiring a lorry, n is the distance covered and a, b are two constants.

Part a).

We have to find the constants a and b.

Now we will find the system of equations to find the value of constants.

The cost of travelling 100 miles is £82.

82 = a + 100b ---------(1)

The cost of travelling 250 miles is £157

157 = a + 250b --------(2)

Now we will subtract equation 2 from 1.

157 - 82 = (a + 250b) - (a + 100b)

75 = 150b

b =  \(\frac{75}{150}=0.5\)

Now we put the value of b in equation 1

82 = a + 100×(0.5)

82 = a + 50

a = 82 - 50 = 32

a = 32 and b = 0.5

Part b).

We have to find the cost of hiring a lorry to travel 300 miles.

C = a + bn

C = 32 + (0.5)(300)

C = 32 + 150

C = £182

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