Challenging equation word problems Please help with these four problems (1 Viewer)

[kpad5991]

a) In triangle PQR, the length of each side is a whole number of centimetres. Also, PQ is 14 cm longer than PR, and QR is 30 cm longer than PR. Find the minimum possible perimeter of triangle PQR in centimetres.

b) A rectangular garden pond has a length 60 cm more than its width. The pond has a 50 cm wide path around its perimeter. If the area of the path is 5.6 m2 , find the width of the pond.

c) A father is concerned about his son’s progress in Mathematics. In order to encourage him, he agrees to give him 10 cents for every problem he solves correctly and to prenalise him 15 cents for every problem he gets wrong. The boy completed 22 problems for homework. How many problems did the girl get correct?


d) When a mathematics teacher was asked her age she replied, “One-fifth of my age three years ago when added to half my age last year gives my age eleven years ago.” How old is she?

 

[Eagle Mum]

Three of these questions (b,c,d) have recently been posed in another thread on this forum and answered, although c) lacks sufficient information to reach a unique solution (https://boredofstudies.org/threads/...-need-working-out-please.394774/#post-7371932).

For a), let ‘L’ be the length PR. Since no side of a triangle can exceed the sum of the lengths of the two other sides:
L + 30 < L + L + 14
L + 30 < 2L + 14
16 < L
Since each side is a whole number of centimetres and the question asks for minimum value(s), L = 17
PR = 17, PQ = 31 and QR = 47
Therefore the minimum perimeter is 95 cm.

ETA: Are these questions really preliminary HSC level? Have they been posted in the correct section?