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!!!!!
Answers
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 =
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
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
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Hope this helps! :)
Answer:
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Step-by-step explanation:
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Happy to Help!