To find the cost of a 9-mile journey, we need to first determine the fixed amount that the taxi firm charges for each journey, and then the amount that they charge per mile. We can do this by setting up the following equations:
For the 4-mile journey:
f + 4p = 5.40
For the 7-mile journey:
f + 7p = 7.80
We can then solve for f and p by substituting the value of f from the first equation into the second equation, giving us:
f + 7p = 7.80
f + 4p = 5.40
Substituting the value of f from the first equation into the second equation, we get:
(f + 4p) + 7p = 7.80
5.40 + 7p = 7.80
Subtracting 5.40 from both sides, we get:
7p = 2.40
Dividing both sides by 7, we get:
p = 0.34
Now that we know the value of p, we can substitute it into the first equation to solve for f:
f + 4p = 5.40
f + 4(0.34) = 5.40
f + 1.36 = 5.40
Subtracting 1.36 from both sides, we get:
f = 5.40 - 1.36
f = 4.04
Now that we know the value of f and p, we can use these values to calculate the cost of a 9-mile journey. The cost of a 9-mile journey is:
f + 9p = 4.04 + 9(0.34) = 4.04 + 3.06 = 7.10
Therefore, a 9-mile journey will cost £7.10.
Answer:
£9.40
Step-by-step explanation:
Given variables:
Defined variables:
1 pound = 100 pence ⇒ 1 pence = 0.01 pounds
Therefore, the equation that models the given scenario is:
[tex]y = 0.01px +f[/tex]
Given:
Substitute the given information into the equation to create two equations:
[tex]\implies f+0.01(4)p=5.40[/tex]
[tex]\implies f+0.01(7)p=7.80[/tex]
Therefore:
[tex]\implies f+0.04p=5.40[/tex]
[tex]\implies f+0.07p=7.80[/tex]
Subtract the first equation from the second to eliminate f:
[tex]\implies 0.03p=2.40[/tex]
Solve for p:
[tex]\implies \dfrac{0.03p}{0.03}=\dfrac{2.40}{0.03}[/tex]
[tex]\implies p=80[/tex]
Substitute the found value of p into one of the equations and solve for f:
[tex]\implies f+0.04(80)=5.40[/tex]
[tex]\implies f+3.20=5.40[/tex]
[tex]\implies f=2.20[/tex]
Substitute the found values of p and f into the equation to create an equation for the cost of x miles:
[tex]\implies y=0.8x+2.2[/tex]
To find the cost of a 9-mile journey, substitute x = 9 into the found equation:
[tex]\implies 0.8(9)+2.2=9.40[/tex]
Therefore, the cost of a 9-mile journey is £9.40.
