v1 Measurement, STD2 M7 2022 HSC 38

A 5.0 L container is filled with a mixture of milk and coffee in the ratio 3:2.

After removing 1.0 L of the mixture, pure milk is added to refill the container.

What is the ratio of milk to coffee in the final mixture? (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

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`17:8`

Show Worked Solution

`text{Original mixture amounts}`

`text{Milk : Coffee = 3000 mL : 2000 mL}`

`text{Removing 1.0 L (1000 mL) removes}`

`text{→ }(3/5)×1000=600\text{ mL milk and }(2/5)×1000=400\text{ mL coffee}`

`text{Milk after removal}`

`=3000-600=2400\text{ mL}`

`text{Coffee after removal}`

`=2000-400=1600\text{ mL}`

`text{After refilling with 1000 mL milk:}`

`text{Milk }=2400+1000=3400\text{ mL}`

`text{Coffee }=1600\text{ mL}`

`:.\ \text{Final ratio } \text{Milk : Coffee}`

`=3400:1600`

`=17:8`

♦♦ Mean mark 34%.