(a) Rice costs \$x/kg and potatoes \$(x + 1)/kg. 12 kg rice and 7 kg potatoes cost \$31.70. Find x. [3]

Small juice bottles cost \$y, large bottles \$(y + 1). Spending \$36 on small bottles gives 25 more bottles than spending \$36 on large bottles.

(b(i)) Show \(25y^2+25y-36=0\). [3]

(b(ii)) Factorise \(25y^2+25y-36\). [2]

(b(iii)) Solve the equation. [1]

(b(iv)) Find the total cost of one small and one large bottle. [1]