E = 15l + 4h,

Question

Jane is planning a trip abroad. Her friend tells her about a formula that she can use to estimate the extra (hidden) costs, E, in pounds, involved in using a budget airline rather than a standard airline. The formula is E = 15l + 4h, where l is the number of pieces of checked luggage that she wishes to take, and h is the number of flying hours for the round trip. (i) Jane plans to fly from Manchester to Paris, a round trip involving 2 hours 55 minutes total flying time, and she would like to take one piece of checked luggage. Use the formula to find the extra cost involved in using a budget airline for such a trip. [3] (ii) Jane finds return flights advertised from Manchester to Paris costing £97 from a budget airline and £117 from a standard airline. Assuming that the formula holds, explain why she would be better off choosing the standard airline. [3] (iii) Airlines offer fares for adults, children and infants, where an adult is anyone aged 12 years or over, and an infant is under 2 years old. Let a represent the age of a child in years. (1) Use a number line to represent the interval between the lowest and highest ages for which a child fare applies. (2) Give a double inequality to describe the age range for which a child fare applies.

Answer 1

E=15l+4h

(i) l=1 and h=3 (the nearest whole number of hours); E=£15+£12=£27. If h can include fractions of hours then 4h=£11.67, so E=£26.67.

(ii) Total cost of the. budget airline=£97+£26.67=£123.67 which is more than the £117 standard fare.

(iii)

(1) --|2---------|12------

(2) 2≤a<12 is age at least 2 years old but under 12 years old.