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RV-08-001 · Changing a ratio by transferring quantities

Two containers A and B hold water in the ratio 8:4. After 20 litres are transferred from A to B, the ratio is 7:5. No water is lost. Work out how many litres were originally in each container.

Ratio: Using ALGEBRAIC Fractions (Transferring Quantities) Booklet p. 20
Method
1) Original amounts ax and bx
2) After transfer: (ax − move) : (bx + move) = new ratio
3) Rewrite as fractions, cross multiply, and solve for x
Worked Example (RV-08-001)
1)
Original quantities: A=8x, B=4xA=8x,\ B=4x.
2)
After transfer: A=8x−20, B=4x+20A=8x-20,\ B=4x+20.
3)
8x−204x+20=75\frac{8x-20}{4x+20}=\frac{7}{5}
4)
Cross multiply: 5(8x−20)=7(4x+20)5(8x-20)=7(4x+20).
5)
40x−100=28x+140⇒12x=240⇒x=2040x-100=28x+140\Rightarrow 12x=240\Rightarrow x=20
6)
Original amounts: A=8(20)=160A=8(20)=160 litres; B=4(20)=80B=4(20)=80 litres.
Ans = A: 160 litres; B: 80 litres.