First
The number of ten-cent coins in a box was 1/2 the number of fifty-cent coins. Syed took out 5 fifty-cent coins and exchanged them for ten-cent coins. Then he put the money back into the box. The number of fifty-cent coins became 5/8 the number of ten-cent coins. How much money was there in the box?
The number of ten-cent coins in a box was 1/2 the number of fifty-cent coins. Syed took out 5 fifty-cent coins and exchanged them for ten-cent coins. Then he put the money back into the box. The number of fifty-cent coins became 5/8 the number of ten-cent coins. How much money was there in the box?
(Before)
10 cents : 50 cents
= 1u : 2u
(After)
10 cents : 50 cents
= 8p : 5p
(Change)
1 × 50 cent coins = 5 × 10 cent coins
loss of 5 × 50 cent coins = gain of 25 × 10 cent coins
(50 cent coins)
2u - 5 = 5p
(10 cent coins)
1u + 25 = 8p
Second
In a bag, the ratio of the number of $2 notes to the number of $10 notes were 3 : 4. Ten $10 notes were removed from the bag to exchange for $2 notes which were then put back into the bag. The total value of money in the bag was unchanged after the exchange. The ratio of the number of $2 notes to the number of $10 notes then became 8 : 3. Find the ratio of the value of the $2 notes to the value of the $10 notes in the bag after the exchange. Leave your answer in its simplest form.
In a bag, the ratio of the number of $2 notes to the number of $10 notes were 3 : 4. Ten $10 notes were removed from the bag to exchange for $2 notes which were then put back into the bag. The total value of money in the bag was unchanged after the exchange. The ratio of the number of $2 notes to the number of $10 notes then became 8 : 3. Find the ratio of the value of the $2 notes to the value of the $10 notes in the bag after the exchange. Leave your answer in its simplest form.
Third
A box contained 50-cent and 20-cent coins in the ratio 2:3.
Some 50-cent coins were taken out and exchanged for 20-cent coins.
The ratio of the number of 50-cent coins to the number of 20-cent coins became 2:7. Find:
The ratio of the number of 50-cent coins to the number of 20-cent coins became 2:7. Find:
a) the total value of money in the box
b) the number of 50-cent coins which were taken to exchange for 20-cent coins.
b) the number of 50-cent coins which were taken to exchange for 20-cent coins.
2 x 0.50 coin = 5 x 0.20 coin
Total Value = $0.50 × 2 units + $0.20 × 3 units = $1.00u + $0.60u = $1.60u
Total Value = $0.50 × 2 parts + $0.20 × 7 parts = $1.00p + $1.40p = $2.40p
1.60u = 2.40p
2u = 3p
3u = 4.5p
0.50 x 3p + 0.20 x 4.5p = 1.5p + 0.6p
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