Challenging Word Problems 001
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John was given $3000 and Nat was given $1000. The document presents two scenarios where John and Nat are spending money each day. By drawing representations of the amounts spent and left over in each scenario, the document determines that each unit represents $500. Therefore, John was given 4 units ($3000) and Nat was given 2 units ($1000).
Challenging Word Problems 001
- 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. (Its 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. Lets 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 : Lets model for the second scenario. This time, John spends 2 times more than Nat. Since in both scenarios, Nat spends all her money, Nats 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, lets 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, lets 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!