Learn to solve challenging word problems in Singapore Maths. This slide uses bar modelling.

1. Challenging
Word
Problems

2. SOLVE THIS!
John and Nat were given some money.
If John spends $50 and Nat spends $100 each day,
John would still have $2500 left while Nat would
have spent all her money.
If John spends $100 and Nat spends $50 each day,
John would still have $1000 left while Nat would
have spent all her money.
How much were John and Nat given each?

3. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500 left
while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000 left
while Nat would have spent all her money.
How much were John and Nat given each?
STEP 1 : Draw an approximation of the amount given to John and Nat. It looks
like John was given more money since he has money left whether he spends
more or less per day compared to Nat. (It’s not important to be exact here)
John
Nat

4. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500
left while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000 left
while Nat would have spent all her money.
How much were John and Nat given each?
STEP 2 : We know Nat spends 2 times more than John in the first scenario.
Let’s draw equal blocks to represent this understanding.
John
Nat
1
1

5. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500
left while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000 left
while Nat would have spent all her money.
How much were John and Nat given each?
STEP 3 : We also know John would have $2500 left, this is represented by the
white bar
John
Nat
$2500
1
1

6. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500 left
while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000
left while Nat would have spent all her money.
How much were John and Nat given each?
STEP 4 : Let’s model for the second scenario. This time, John spends 2 times more
than Nat. Since in both scenarios, Nat spends all her money, Nat’s yellow bar
would still be the same length, and John would have 2 times as many squares
John
Nat
$2500
John
Nat
1
2
1
2

7. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500 left
while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000
left while Nat would have spent all her money.
How much were John and Nat given each?
STEP 5 : In scenario 2, we know John would have $1000 left, this is again
represented by the white bar
John
Nat
$2500
John
Nat
1
2
1
2
$1000

8. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500 left
while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000 left
while Nat would have spent all her money.
How much were John and Nat given each?
STEP 6 : At this point, we can compare the 2 scenarios for John and find the value
for each block! Can you find it?
John
Nat
$2500
John
Nat
1
2
1
2
$1000

9. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500 left
while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000 left
while Nat would have spent all her money.
How much were John and Nat given each?
STEP 7 : First, compare the white block in scenario 1 with the same length in
scenario 2. We can tell that 3 Units + $1000 = $2500.
John
Nat
$2500
John
Nat
1
2
1
2
3 Units $1000
1 Unit 1 Unit 1 Unit
$1000

10. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500 left
while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000 left
while Nat would have spent all her money.
How much were John and Nat given each?
STEP 8 : Therefore,
3 Units = $2500-$1000 = $1500.
1 Unit = $1500 / 3 = $500
John
Nat
$2500
John
Nat
1
2
1
2
3 Units $1000
1 Unit 1 Unit 1 Unit
$1000

11. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500 left
while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000 left
while Nat would have spent all her money.
How much were John and Nat given each?
STEP 8 : Since we draw equal units, we can easily calculate John was given
4 units + $1000 = (4 X $500) + $1000 = $3000
John
Nat
$2500
John
Nat
1
2
1
2
1 Unit 1 Unit 1 Unit 1 Unit
$1000
$3000

12. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500 left
while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000 left
while Nat would have spent all her money.
How much were John and Nat given each?
STEP 9 : And for Nat, she has 2 units X $500 = $1000
John
Nat
$2500
John
Nat 1 Unit 1 Unit
1
2
1
2
1 Unit 1 Unit 1 Unit 1 Unit
$1000
$3000
$1000

13. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500
left while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000 left
while Nat would have spent all her money.
How much were John and Nat given each?
STEP 10 : Now, let’s check our answers by applying the answers to the original
scenarios.
1
2
Scenario 1 :
Nat has $1000, and spends $100 per day. She will take 10 days to spend $1000.
In 10 days, John would spend $50 X 10 days = $500, and have $2500 left. This adds
up to $3000 which matches our answer.

14. John and Nat were given some money.
If John spends $50 and Nat spends $100 each day, John would still have $2500 left
while Nat would have spent all her money.
If John spends $100 and Nat spends $50 each day, John would still have $1000
left while Nat would have spent all her money.
How much were John and Nat given each?
STEP 10 : Now, let’s check our answers by applying the answers to the original
scenarios.
1
2
Scenario 1 :
Nat has $1000, and spends $100 per day. She will take 10 days to spend $1000.
In 10 days, John would spend $50 X 10 days = $500, and have $2500 left. This adds
up to $3000 which matches our answer.
Scenario 2 :
Nat has $1000, and spends $50 per day. She will take 20 days to spend $1000.
In 20 days, John would spend $100 X 20 days = $2000, and have $1000 left. This
again adds up to $3000 which matches our answer. So we can safely say our
answer is correct!