Daniel kept some $1 coins and some 20-cent coins in a tin. He had 3 more $1 coins than 20-cent coins. After he used 5 of the $1 coins to pay for a notebook, the value of the $1 coins left was $7.60 more than the value of the 20-cent coins.
- How many 20-cent coins did Daniel have?
- What was the total value of all his coins at first? Give your answer in dollars.
Need a hint?
After he uses 5 of the $1 coins, how many fewer $1 coins than 20-cent coins does he have? Match each $1 coin with a 20-cent coin and find the difference in value for each pair.
Worked answer
- (a) At first: $1 coins = 20-cent coins + 3. After using 5, he has 2 fewer $1 coins than 20-cent coins.
- Match each $1 coin left with a 20-cent coin. The 20-cent coins have 2 extra coins, worth 2 × 20 = 40 cents.
- Each matched pair has a difference of 100 - 20 = 80 cents. $7.60 = 760 cents.
- The matched pairs make 760 + 40 = 800 cents more, since the 40 cents of extra 20-cent coins must be made up.
- Number of pairs = 800 ÷ 80 = 10. So there are 10 $1 coins left and 10 + 2 = 12 20-cent coins.
- (b) $1 coins at first = 10 + 5 = 15, worth $15.
- 20-cent coins: 12 × $0.20 = $2.40.
- Total value = $15 + $2.40 = $17.40.
The mistake this question tests
Left out the units
Many pupils forget the 2 extra 20-cent coins that have no $1 coin to match, so they divide 760 by 80 and get a number that is not whole, or they treat the number of pairs as the number of 20-cent coins.
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