Question

A taxi firm charges a fixed amount of £f, for each journey and then p pence a mile. A 4-miles journey costs £5.40 A 7-miles journey costs £7.80 How much will a 9-miles journey cost?​

Answer 1

£9.40

Explanation:

Given variables:

• f = fixed amount for each journey (in pounds)
• p = pence per mile

Defined variables:

• Let x = number of miles.
• Let y = total cost (in pounds).

1 pound = 100 pence ⇒ 1 pence = 0.01 pounds

Therefore, the equation that models the given scenario is:

`y = 0.01px +f`

Given:

• A 4-mile journey costs £5.40
• A 7-mile journey costs £7.80

Substitute the given information into the equation to create two equations:

`\implies f+0.01(4)p=5.40`

`\implies f+0.01(7)p=7.80`

Therefore:

`\implies f+0.04p=5.40`

`\implies f+0.07p=7.80`

Subtract the first equation from the second to eliminate f:

`\implies 0.03p=2.40`

Solve for p:

`\implies (0.03p)/(0.03)=(2.40)/(0.03)`

`\implies p=80`

Substitute the found value of p into one of the equations and solve for f:

`\implies f+0.04(80)=5.40`

`\implies f+3.20=5.40`

`\implies f=2.20`

Substitute the found values of p and f into the equation to create an equation for the cost of x miles:

`\implies y=0.8x+2.2`

To find the cost of a 9-mile journey, substitute x = 9 into the found equation:

`\implies 0.8(9)+2.2=9.40`

Therefore, the cost of a 9-mile journey is £9.40.