An art shop had crayon sets and paint sets in the ratio 4 : 7 at first. The shop sold 12 paint sets and received 18 more crayon sets. After this, the number of crayon sets was equal to the number of paint sets. How many art sets were there altogether at first?
Need a hint?
Write the amounts after the change in units, then set the two equal. Find the value of one unit before adding up.
Worked answer
- At first, crayon sets : paint sets = 4 units : 7 units.
- After the change: crayon = 4 units + 18, paint = 7 units − 12.
- The two are equal, so 4 units + 18 = 7 units − 12.
- 3 units = 30, so 1 unit = 10.
- At first there were 4 × 10 = 40 crayon sets and 7 × 10 = 70 paint sets.
- Total at first = 40 + 70 = 110 sets.
Answer: 110 sets
The mistake this question tests
Habit
Stopped at one part in ratio
Many pupils find 3 units = 30 and stop there, or treat 30 as one unit and get a total that is too large.
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See the answer →Practise PSLE ratio until the mistakes stop.
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