(a) Amir buys 3 cakes at c cents each and 2 loaves at (2c − 11) cents each, spending \$5.87. Find c. [3]

(b) Water costs \$w and juice \$(w + 1) per bottle. Alex spends \$22 on water and \$42 on juice, buying equal numbers of each. Find w. [3]

(c(i)) Alicia walks 9 km at x km/h then runs 5 km at (2x + 1) km/h. Total time is 2.5 h. Show \(10x^2-41x-18=0\). [4]

(c(ii)) Find Alicia’s running speed, showing working. [4]