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 & $\gamma$ \
Shopping at Akihabara & 262.49 & $ \
Onsen visit & 6,811 & $\gamma$ \
Museum visit & 2,423 & $\gamma$ \
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 expenses amount to about $586.68, which exceeds his budget of $575 by $11.68. Therefore, he cannot afford to attend the sumo tournament. The correct answer is option d: Hector cannot afford to see the sumo tournament, because it would put him over budget by approximately $11.68.
;
Calculate the total cost of activities in US dollars: $74.95 + 262.49 = $337.44.
Calculate the total cost of activities in Japanese yen: 8745 + 6811 + 2423 + 5488 = 23467 yen.
Convert the total cost in Japanese yen to US dollars: $\frac{23467}{94.153} \approx $249.24.
Calculate the total cost of all activities in US dollars: $337.44 + 249.24 = $586.68. Since Hector's budget is $575, he is over budget by $586.68 - $575 = $11.68. Therefore, Hector cannot afford the sumo tournament.
The final answer is: Hector cannot afford to see the sumo tournament, because it would put him over budget by $\boxed{ 11.68} .
Explanation
Calculate total cost in USD First, let's calculate the total cost of the activities in US dollars. Hector plans to spend $74.95 on a Kabuki performance and $262.49 on shopping at Akihabara. So the total cost in US dollars is:
Summing USD costs 74.95 + 262.49 = 337.44
Calculate total cost in JPY Next, let's calculate the total cost of the activities in Japanese yen. Hector plans to spend ¥8,745 on a Kaiseki dinner, ¥6,811 on an Onsen visit, ¥2,423 on a Museum visit, and ¥5,488 on a Sumo tournament. So the total cost in Japanese yen is:
Summing JPY costs 8745 + 6811 + 2423 + 5488 = 23467
Convert JPY to USD Now, let's convert the total cost in Japanese yen to US dollars using the given conversion rate of 1 USD = 94.153 JPY.
Performing the conversion 94.153 23467 ≈ 249.24
Calculate total cost in USD Now, let's calculate the total cost of all activities in US dollars by adding the cost of activities already in USD and the converted cost from JPY to USD.
Summing all costs in USD 337.44 + 249.24 = 586.68
Compare total cost with budget Finally, let's compare the total cost with Hector's budget to determine if he can afford all the activities. Hector's budget is $575.
Calculating the difference 575 − 586.68 = − 11.68
Final Answer Since the result is negative, Hector cannot afford to see the sumo tournament. He is over budget by $11.68. Therefore, the correct answer is: d. Hector cannot afford to see the sumo tournament, because it would put him over budget by approximately $11.68.
Examples
Budgeting is a crucial skill in personal finance. For example, if you're planning a road trip, you need to estimate costs for gas, accommodation, food, and activities. By converting all expenses to a single currency (like USD) and comparing the total to your budget, you can determine if the trip is affordable or if adjustments are needed. This ensures you don't overspend and can enjoy your trip without financial stress. Similar calculations are used in project management to ensure projects stay within budget.
