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For any given journey, ABC Taxis charge customers a base fare of £5 plus 80p per mile. XYZ Taxis charge a base fare of £3 plus £1.20 per mile. Find the number of miles, x, that must be traveled in order for ABC taxis to be the cheaper journey option.

This question can represented in algebraic form: ABC Taxis = 0.8x + 5XYZ Taxis = 1.2x + 3 Noting that the units must be consistent throughout the question, so we have changed the pence into miles. (80p = £0....
EM
Answered by Euan M. • Maths tutor
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Determine (27/8)^3/2

Understanding we can split it into numerator and denominator and find individually.Understanding that ^1/3 is same as cube root and why, by considering that ^2 is squaring27^2/3 = 3^2 = 98^2/3 = 2^2 = 4 =9/4
JT
Answered by James T. • Maths tutor
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Solve the simultaneous equations for x and y: 3x+2y = 14 and 5x-y = 6

3x + 2y = 14 -> 15x - y = 6 -> 2Answer: x = 2 and y =4Solution:multiply both sides of equation 2 by 2: 10x - 2y = 12add this to equation 1: 3x + 10x + 2y -2y = 14 +12simplify: 13x = 26divide by 13: x =...
MF
Answered by Megan F. • Maths tutor
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x - 2y = 1 , x^2 + y^2 = 13 find the solutions to this quadratic equation

equation 1) x - 2y = 1equation 2) x 2 + y 2 = 13 Rearrange equation 1 to: x = 1+2ysubstitute into equation 2: (1+2y) 2 + y 2 =13expand first bracket: (1+2y)(1+2y) +y 2 =13(1+4y+4y 2 ) +y 2 = 13Collect like t...
CS
Answered by Caitlin S. • Maths tutor
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solve y=3x+4, x=y+1

Equation 1) y=3x+4Equation 2) y=x+1 Rearrange equation 2 into terms of x as this is the simplest: x= y-1 (We do this by subtracting 1 off of each side to get X by itself)Substitute new equation 2 into 1: y=3...
CS
Answered by Caitlin S. • Maths tutor
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