A taxi company charges a fixed hire fee (which is a whole number of dollars) plus a rate for each
kilometer (which is a multiple of 10¢ and more than the set national minimum rate of $1.75),
rounded up to the nearest kilometer.
Maira’s last journey cost $37.90, but she does not know how far it was, or what the fixed hire fee
is. She wants to know how far the journey was.

She has a previous bill from the same taxi company, for a different journey, for $21.80.
How far was her last journey?

362 kilometre

Step-by-step explanation:

Let a be the total cost of a journey

let b represent the total distance of a journey

$1.75 is a fixed charge of a journey

the additional charge is $0.10 for b distance ,hence total of additional charge is $.10 multiplied by b i.e 0.1 b

a=1.75+0.1b

a =37.90

37.90=1.75+0.1b

0.1b=37.90-1.75

0.1 b=36.15

b=36.15 /0.10

b=361.5

b=362 kilometre

For the journey that cost 21.80

21.80=1.75+0.1 b

0.1 b=21.80-1.75

0.1 b=20.05

b=20.05 /0.1

b=200.5

b =201 kilometre

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629