Hector is on a trip to Japan. The table below outlines some of the fun things he would like to see and do while on his trip, as well as their estimated costs, either in US dollars ($) or Japanese yen (¥). Hector has $575 budgeted for expenses like this.
| Item | Cost | Currency |
| ------------------------ | ------- | -------- |
| Kabuki performance | 74.95 | $ |
| Kaiseki dinner | 8,745 | ¥ |
| Shopping at Akihabara | 262.49 | $ |
| Onsen visit | 6,811 | ¥ |
| Museum visit | 2,423 | ¥ |
Hector would also like to see a professional sumo tournament while he is there, which would cost him ¥5,488. If the conversion rate of US dollars to Japanese yen is 1:94.153 at the time of Hector's trip, how will this affect his budget?
A. Hector can see the sumo tournament and have about $322 left over.
B. Hector can see the sumo tournament and have about $86 left over.
C. Hector has exactly enough left in his budget to see the sumo tournament.
D. Hector cannot afford to see the sumo tournament, because it would put him over budget by...
Answer (2)
Hector's total estimated expenses for his planned activities in Japan amount to approximately $586.69. Since his budget is $575, he is over budget by about $11.69. Therefore, Hector cannot afford to see the sumo tournament within his current budget.
;
Calculate the total expenses in USD: Kabuki performance and Akihabara shopping sum to $337.44.
Convert the sumo tournament cost to USD: ¥5,488 is approximately $58.29.
Convert other expenses in Yen to USD: Kaiseki dinner, Onsen visit and Museum visit sum to approximately $190.96.
Calculate the total expenses and compare with the budget: Hector is over budget by approximately $\boxed{ 11.69} .
Explanation
Calculate expenses in USD First, let's identify the costs in US dollars. Hector has two expenses directly in US dollars: the Kabuki performance at $74.95 and shopping at Akihabara for $262.49. The sum of these expenses is:
Sum of USD expenses 74.95 + 262.49 = 337.44
Convert Sumo cost to USD Next, we need to convert the cost of the sumo tournament from Yen to US dollars. The sumo tournament costs ¥5,488, and the conversion rate is 1 USD to ¥94.153. So, the cost in USD is:
Sumo cost in USD 94.153 5488 ≈ 58.29
Total expenses in USD Now, let's calculate Hector's total expenses in USD, including the Kabuki performance, shopping, and the sumo tournament:
Sum of all expenses 337.44 + 58.29 = 395.73
Remaining budget Hector's budget is $575. To find out how much he has left after these expenses, we subtract the total expenses from his budget:
Calculate remaining amount 575 − 395.73 = 179.27
Recalculating with all expenses Therefore, Hector can see the sumo tournament and will have approximately $179.27 left over. This is closest to option b, which states he'd have about 86 l e f t o v er . Ho w e v er , o u rc a l c u l a t i o n s h o w s h e ha ss i g ni f i c an tl y m ore . L e t ′ sre − e x amin e t h e p ro b l e m t o mak es u re w e d i d n ′ t mi ss an y t hin g . T h eo t h ere x p e n ses inY e na re t h eK ai se ki d inn er ( ¥ 8 , 745 ) , O n se n v i s i t ( ¥ 6 , 811 ) , an d M u se u m v i s i t ( ¥ 2 , 423 ) . I f w eco n v er t a ll o f t h ese t o U S D , w e ha v e : K ai se ki d inn er : \frac{8745}{94.153} \approx 92.88 O n se n v i s i t : \frac{6811}{94.153} \approx 72.34 M u se u m v i s i t : \frac{2423}{94.153} \approx 25.74 S u m o t o u r nam e n t : \frac{5488}{94.153} \approx 58.29$
Total in USD: 92.88 + 72.34 + 25.74 + 58.29 = 249.25 Total expenses: 337.44 + 249.25 = 586.69 Remaining budget: $575 - 586.69 = -11.69
Final Answer Since Hector's total expenses are $586.69 and his budget is $575, he is over budget by $11.69. Therefore, Hector cannot afford to see the sumo tournament, because it would put him over budget by approximately $11.69.
Examples
Budgeting is a crucial skill in personal finance. This problem demonstrates how to manage a budget when dealing with multiple currencies and expenses. Understanding conversion rates and tracking spending helps ensure financial stability and prevents overspending, whether you're planning a trip or managing your daily finances.
