Olivia made some biscuits. She sold ⁴₅ of them in the afternoon and ³₄ of the remainder in the evening. If she sold 65 more biscuits in the afternoon than in the evening, how many biscuits did she make altogether?

Afternoon	Remainder		Total
4x4	1x4		5x4
	Evening	Left
	3	1
16 u	3 u	1 u	20 u

Fraction of biscuits left after selling some in the afternoon
= 1 - ⁴₅ 
= ¹₅

Fraction of biscuits sold in the evening
= ³₄ x ¹₅
= ³₂₀

Make the denominators the same.
 ⁴₅ = ¹⁶₂₀ 

Number of biscuits that Olivia sold in the afternoon = 16 u
Number of biscuits that Olivia sold in the evening = 3 u

Number of more biscuits that Olivia sold in the afternoon than in the evening
= 16 u - 3 u
= 13 u

13 u = 65

1 u = 65 ÷ 13 = 5

Total number of biscuits that Olivia made
= 20 u
= 20 x 5
= 100

Answer(s): 100