Sack P and sack Q contained 1150 kg of rice altogether. Sack P contained more rice than sack Q. Then 230 kg of rice were poured into sack Q, and sack P now had 60 kg more rice than sack Q.
- How many kilograms more rice did sack P contain than sack Q at first?
- How many kilograms of rice did sack Q contain at first?
Need a hint?
In (a), the 230 kg added to sack Q is still part of the gap after pouring, so add it back to the 60 kg. In (b), use the total and the difference like a bar model: add them, then halve to find the larger sack.
Worked answer
- (a) After pouring, P minus (Q + 230) = 60, so P minus Q at first = 60 + 230 = 290 kg.
- (b) P + Q = 1150 and P - Q = 290, so 2 x P = 1150 + 290 = 1440.
- P = 1440 ÷ 2 = 720 kg, so Q = 1150 - 720 = 430 kg.
The mistake this question tests
Found the increase, not the new price
Pupils treat the 60 kg as the difference at first and forget that the 230 kg poured into Q must be added back, so they get 60 instead of 290 for the difference.
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