SOLUTION: In his demonstration on the art of tea making, John first poured some tea from a pot into an empty cup. The amount of tea in the cup is 1/4 of the amount of tea left in the pot. F

Question 1203827: In his demonstration on the art of tea making, John first poured some tea from a pot into an empty cup.
The amount of tea in the cup is 1/4 of the amount of tea left in the pot. For the second step, he poured 20 ml of milk into the cup. Finally, he poured 50 ml of tea from the pot into the cup. The final amount of liquids in the cup was 1/3 of that left in the pot.
(a) Find the total amount of milk and tea added from the second and final steps.
(b) Find the original amount of tea in the pot.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the amount of tea in the pot to start.
let y = the amount of tea poured into the cup.

the amount of tea left in the top = x - y
the amount of tea in the cup is equal to 1/4 * the amount of tea remaining in the pot.
that gets you y = 1/4 * (x - y)
simplify to get y = 1/4 * x - 1/4 * y
add 1/4 * y to both sides of that equation to get y + 1/4 * y = 1/4 * x
combine like terms to get 5/4 * y = 1/4 * x
solve for y to get y = 4/5 * 1/4 * x = 1/5 * x.

you have y = 1/5 * x.
this means that the amount of tea left in the pot is 4/5 * x and the amount of tea in the cup is 1/5 * x.

you add 50 ml of milk to the cup and then add 50 ml ot tea to the cup that you took from the pot.

the pot now as 4/5 * x - 50 ml while the cup has 1/5 * x + 70 ml.

the amount of liquid in the cup is equal to 1/3 * the amount of liquid left in the pot.

that means that 1/5 * x + 70 = 1/3 * (4/5 * x - 50)
simplify to get 1/5 * x + 70 = 1/3 * 4/5 * x - 1/3 * 50.
simplify further to get 1/5 * x + 70 = 4/15 * x - 50/3.
multiply both sides of the equation by 15 to get:
15/5 * x + 70 * 15 = 4/15 * 15 * x - 15 * 50/3
simplify to get:
3 * x + 1050 = 4 * x - 250.
subtract 3 * x from both sides of the equation and add 250 to both sides of the eqution to get:
1050 + 250 = x
combine like terms to get:
1300 = x.

x = 1300 means that the original amount of tea in the pot is 1300 ml.
after pouring tea from the pot to the cup, you have 4/5 * 1300 tea left in the pot and 1/3 * 1300 tea in the cup.
that equals 1040 ml of tea left in the pot with 260 ml of tea in the cup.
you add 70 ml of liquid to the cup to get 260 + 70 = 330 ml of liquid in the cup.
you subtract 50 ml of tea from the pot to get 1040 - 50 = 990 ml of tea left in the pot.

330 / 990 is equal to 1/3.
the amount of liquid in the cup is 1/3 * the amount of tea left in the pot.
this agrees with what you are given, confirming the solution is correct.

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