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QUESTION: A jar 1/6 filled with beads has a mass of 2 1/2 kg. When it is completely filled with beads, it has a mass of 6 1/2 kg. What is the mass of the empty jar?

ANSWER: "A jar 1/6 filled with beads has a mass of 2 1/2 kg. When it is completely filled with beads, it has a mass of 6 1/2 kg."

jar + beads = 6.5 kg

jar + (1/6)beads = 2.5 kg

subtract the second equation from the first:

(5/6) beads = 4 kg

beads = 4×6/5 = 4.8 kg

jar = 6.5 kg - 4.8 kg = 1.7 kg

---------- FOLLOW-UP ----------

QUESTION: "James gave 1/4 of his money to his mother. He spent 5/18 of the remainder on a wallet and 2 CDs and had $78 left. The wallet cost 4 times as much as a CD.

(a) How much money did James have at first?

(b) What was the cost of one CD?"

x = starting amount of money

"James gave 1/4 of his money to his mother."

He had (3/4)x remaining.

"He spent 5/18 of the remainder on a wallet and 2 CDs and had $78 left."

(13/18)(3/4)x = $78

x = $144

James started out with $144.

:::::

The wallet and 2CDs cost (5/18)(3/4)x = $30.

"The wallet cost 4 times as much as a CD."

The wallet and 2CDs cost as much as 6 CDs.

One CD cost $30/6 = $5.

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