 # Question

Hi! I am new here and I have a question that I don’t know how to answer. Please help!

Lisa has some 50 cent coins and 20 cent coins in the ratio if 2:3. She exchanged six 50cent coins for 20 cent coins. If the ratio of 50cents coins to 20cents coind became 2:5, find the amount of money Lisa had.

I would be grateful if you could provide me with a solution or some steps. Thanks!

Source: CHIJ Primary Toa Payoh

Another possible solution:
by looking at the ratio of the values of the coins.

Before: value of 50cents coins :20 cents coins= 2×50:20×3 =100:60=5:3
after: 2×50:5×20 = 100:100= 1:1
6 50cents coins were exchanged for some 20cents coins…that means total values remained the same.

before: 5u:3u
After: 4u:4u
thus iu = 6×50 =300
total value = 8u =2400 cents =\$24.

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Lisa has some 50 cent coins and 20 cent coins in the ratio if 2 : 3. She exchanged six 50 cent coins for 20 cent coins. If the ratio of 50 cents coins to 20 cents coins became 2 : 5, find the amount of money Lisa had.

50-cent coins : 20-cent coins
2u : 3u

six 50-cent coins ——- 15 20-cent coins
2u – 6 ——- 2p
1u – 3 ——- 1p
3u + 15 ——- 5p = 5 x (1u – 3 ) = 5u – 15
1u ——- (15 + 15)/(5 – 3) = 15
2 x 15 x 0.50 = 15
3 x 15 x 0.20 = 9
9 + 15 = 24

Ans : \$24.

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At first, no. 50 cts coin = 2 units, no of  20 cts coin =3 units

At end, no. 50 cts coin = 2 parts, no of  20 cts coin =5 parts

Six 50 cts coin => fifteen 20 cts coin.

2 units – 6 = 2 parts  –> Eqn (1)

3 units +15 = 5 parts  –> Eqn (2)

10 units – 30 = 10 parts –> Eqn (1) x 5

6 units + 30 = 10 parts –> Eqn (2) x 2

10 units – 30 = 6 units + 30

4 units = 60

1 unit = 15.

At first, she has 30 50cts coins & 45 20cts coins.

30 x \$0.50 + 45 x \$0.20 = \$24

Amount of money Lisa has is \$24

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