Lets get lost in Japan
Introduction
Sakura and Asahi are planning to travel to Japan to visit family there. They plan to be in Japan for two months, (May, June) and during that time take a three week tour around Japan by train.
This activity requires you to calculate the maximum amount of money Sakura and Asahi will need to save for their trip and how long it will take them to save it.
Show your calculations. Use correct mathematical statements. Clearly communicate your strategy and method at each stage of the solution. You will be assessed on the quality of your discussion and reasoning, and how well you link this to the context.
Sakura and Asahi are planning to travel to Japan to visit family there. They plan to be in Japan for two months, (May, June) and during that time take a three week tour around Japan by train.
This activity requires you to calculate the maximum amount of money Sakura and Asahi will need to save for their trip and how long it will take them to save it.
Show your calculations. Use correct mathematical statements. Clearly communicate your strategy and method at each stage of the solution. You will be assessed on the quality of your discussion and reasoning, and how well you link this to the context.
Task
Use the following information to find out how much money Sakura and Asahi will need to save and how long it will take them to save it.
Use the following information to find out how much money Sakura and Asahi will need to save and how long it will take them to save it.
- Sakura and Asahi estimate that for each day they are in Japan, between them they will need on average NZ$180 (to the nearest $40) when they are not on the tour.
- Sakura earns $740 each week. Asahi earns $690 each week. Sakura is able to save three fifths of her income and Asahi, 64% of his income to put towards the trip.
- The cost for the return air tickets is $1200 each. The credit card surcharge is 2.5%
- The cost of travel insurance is $335 plus GST (15%) for the two of them.
- The three week tour costs 383150 Japanese Yen per person.
- Yen are used as currency in Japan.
- The Exchange rate is: 1 NZ Dollar = 76.63 Yen
Sakura's savings:
740x3/5=$444.00
Asahi's Savings:
690x0.64=$441.60
Total: 444+441.6=$885.60
Train Trip:
383150x2/76.63=$10000
740x3/5=$444.00
Asahi's Savings:
690x0.64=$441.60
Total: 444+441.6=$885.60
Train Trip:
383150x2/76.63=$10000
Merit
Tickets
1200x2x1.025=$2460
Insurance
335x1.15=$385.25
Average Daily Allowance May and June comes to 61 days, take away 21 days while on bus trip. (That's where the 40 comes from, not from "to the nearest $40"
40 x 180=$7,200
Total costs= 7200+385.25+2460+10000=$20045.25
Time to save = 20045.25/885.60=22.6347 weeks
=23 whole weeks
Therefore, they will have to save for about 23 weeks.
Tickets
1200x2x1.025=$2460
Insurance
335x1.15=$385.25
Average Daily Allowance May and June comes to 61 days, take away 21 days while on bus trip. (That's where the 40 comes from, not from "to the nearest $40"
40 x 180=$7,200
Total costs= 7200+385.25+2460+10000=$20045.25
Time to save = 20045.25/885.60=22.6347 weeks
=23 whole weeks
Therefore, they will have to save for about 23 weeks.
Adjusting Exchange rate
It is possible that the exchange rate
Might change due to economic conditions, for example it might go from 76.63 to 86.63.
383150x2/86.63=8845.6655
=$8845.67
Total costs= 7200+385.25+2460+8845.67=$18890.92
18890.92/885.60=21.3312
=22 whole weeks.
Therefore an increase in the exchange rate by the stated amount will shorten the time to save by about 1 week.
It is possible that the exchange rate
Might change due to economic conditions, for example it might go from 76.63 to 86.63.
383150x2/86.63=8845.6655
=$8845.67
Total costs= 7200+385.25+2460+8845.67=$18890.92
18890.92/885.60=21.3312
=22 whole weeks.
Therefore an increase in the exchange rate by the stated amount will shorten the time to save by about 1 week.
Normal Excellence
Min daily allowance = 180 -20=160
160 x 40=$6,400
Total costs = 6400+385.25+2460+10000=$19245.25
Time to save = 19245.25/885.60=21.73
=22 weeks
Max daily allowance = 180 +19=$199
199 x 40=$7,960
Total costs = 7960+385.25+2460+10000=$20805.25
Time to save = 20805.25/885.60=23.4928
=24 whole weeks
Therefore it will take them about 22 to 24 whole weeks to save for their trip. This would be 1 week earlier or 1 week later than previously calculated.
Min daily allowance = 180 -20=160
160 x 40=$6,400
Total costs = 6400+385.25+2460+10000=$19245.25
Time to save = 19245.25/885.60=21.73
=22 weeks
Max daily allowance = 180 +19=$199
199 x 40=$7,960
Total costs = 7960+385.25+2460+10000=$20805.25
Time to save = 20805.25/885.60=23.4928
=24 whole weeks
Therefore it will take them about 22 to 24 whole weeks to save for their trip. This would be 1 week earlier or 1 week later than previously calculated.