Question

1. donald purchases a pair of socks, a pair of pants, and a tie. how much money would he need if the sales tax was 8%?
2. paul purchases a belt, a pair of pants, and a sweater. how much change will he get back from $80.00?
3. sandra purchases a pair of socks, a jacket, and a tie. what will her change be if she pays $55.00?
4. if adam wanted to buy a shirt, a pair of socks, a jacket, and a pair of pants, how much money would he need if the items were reduced by twelve percent?
5. brian wants to buy a tie, a bathing suit, and a pair of socks. how much will it cost him?
6. what is the total cost of a jacket, a sweater, and a tie if the items are on sale for twelve percent off the regular price?
7. audrey purchases a pair of pants, a shirt, and a belt. how much change will she get back from $60.00?
8. billy purchases a tie, a jacket, a bathing suit, and a sweater. how much money would he need if the items were reduced by twelve percent?
9. jennifer wants to buy a hat, a t - shirt, a pair of pants, and a tie. how much will she have to pay?
10. janet purchases a belt, a sweater, a pair of pants, and a bathing suit. how much would it cost her if there was a twelve percent discount?
11. if sharon wanted to buy a belt, a hat, and a pair of socks, how much would it cost her?

Explanation:

To solve these problems, we need the regular prices of each item (socks, pants, tie, belt, sweater, jacket, shirt, bathing suit, hat, t - shirt) which are not provided in the given image. Without this information, we can't calculate the total cost, change, or cost after discount for each of these problems.

For example, let's take problem 5: Donald purchases a pair of socks, a pair of pants, and a tie. To find out how much money he needs with an 8% sales tax, we would first need to know the regular prices of socks (\(P_{socks}\)), pants (\(P_{pants}\)) and tie (\(P_{tie}\)). Then we would calculate the subtotal as \(Subtotal=P_{socks} + P_{pants}+P_{tie}\), and the total cost with tax would be \(Total = Subtotal\times(1 + 0.08)\) (since 8% tax means we pay 100% + 8% = 108% of the subtotal). But without the values of \(P_{socks}\), \(P_{pants}\) and \(P_{tie}\), we can't compute the result.

Similarly, for problems involving discounts (like 12% off), we would use the formula \(Discounted\ price=Regular\ price\times(1 - 0.12)\) for each item, sum them up, and then apply tax if applicable. But again, the regular prices are missing.

If you can provide the regular prices of each item, we can solve these problems step - by - step using the following general approach:

General Step - by - Step Approach for Each Problem:

For problems with sales tax (e.g., problem 5):

1. Calculate the subtotal: Add the regular prices of the items being purchased. Let the prices of the items be \(P_1,P_2,\cdots,P_n\). Then \(Subtotal=\sum_{i = 1}^{n}P_i\)
2. Calculate the total with tax: Multiply the subtotal by \((1 + tax\ rate)\). If the tax rate is \(r\) (expressed as a decimal), then \(Total = Subtotal\times(1 + r)\)

For problems with discount (e.g., problem 8, 10, 12, 14):

1. Calculate the discounted price for each item: For an item with regular price \(P\) and discount rate \(d\) (expressed as a decimal), the discounted price is \(P_d=P\times(1 - d)\)
2. Calculate the subtotal of discounted prices: Sum up the discounted prices of all items: \(Subtotal_d=\sum_{i = 1}^{n}P_{d_i}\)
3. If there is tax, calculate the total with tax: Multiply the subtotal of discounted prices by \((1 + tax\ rate)\)

For problems with change (e.g., problem 6, 7, 11):

1. Calculate the total cost of the items (using either the regular price, discounted price with tax if applicable, following the steps above)
2. Calculate the change: Subtract the total cost from the amount paid. If the amount paid is \(A\) and the total cost is \(C\), then \(Change = A - C\)

Since the necessary information (regular prices of items) is not provided, we can't give a numerical answer for any of these problems. Please provide the regular prices of each item to proceed with the calculations.

Answer:

To solve these problems, we need the regular prices of each item (socks, pants, tie, belt, sweater, jacket, shirt, bathing suit, hat, t - shirt) which are not provided in the given image. Without this information, we can't calculate the total cost, change, or cost after discount for each of these problems.

For example, let's take problem 5: Donald purchases a pair of socks, a pair of pants, and a tie. To find out how much money he needs with an 8% sales tax, we would first need to know the regular prices of socks (\(P_{socks}\)), pants (\(P_{pants}\)) and tie (\(P_{tie}\)). Then we would calculate the subtotal as \(Subtotal=P_{socks} + P_{pants}+P_{tie}\), and the total cost with tax would be \(Total = Subtotal\times(1 + 0.08)\) (since 8% tax means we pay 100% + 8% = 108% of the subtotal). But without the values of \(P_{socks}\), \(P_{pants}\) and \(P_{tie}\), we can't compute the result.

Similarly, for problems involving discounts (like 12% off), we would use the formula \(Discounted\ price=Regular\ price\times(1 - 0.12)\) for each item, sum them up, and then apply tax if applicable. But again, the regular prices are missing.

If you can provide the regular prices of each item, we can solve these problems step - by - step using the following general approach:

General Step - by - Step Approach for Each Problem:

For problems with sales tax (e.g., problem 5):

1. Calculate the subtotal: Add the regular prices of the items being purchased. Let the prices of the items be \(P_1,P_2,\cdots,P_n\). Then \(Subtotal=\sum_{i = 1}^{n}P_i\)
2. Calculate the total with tax: Multiply the subtotal by \((1 + tax\ rate)\). If the tax rate is \(r\) (expressed as a decimal), then \(Total = Subtotal\times(1 + r)\)

For problems with discount (e.g., problem 8, 10, 12, 14):

1. Calculate the discounted price for each item: For an item with regular price \(P\) and discount rate \(d\) (expressed as a decimal), the discounted price is \(P_d=P\times(1 - d)\)
2. Calculate the subtotal of discounted prices: Sum up the discounted prices of all items: \(Subtotal_d=\sum_{i = 1}^{n}P_{d_i}\)
3. If there is tax, calculate the total with tax: Multiply the subtotal of discounted prices by \((1 + tax\ rate)\)

For problems with change (e.g., problem 6, 7, 11):

1. Calculate the total cost of the items (using either the regular price, discounted price with tax if applicable, following the steps above)
2. Calculate the change: Subtract the total cost from the amount paid. If the amount paid is \(A\) and the total cost is \(C\), then \(Change = A - C\)

Since the necessary information (regular prices of items) is not provided, we can't give a numerical answer for any of these problems. Please provide the regular prices of each item to proceed with the calculations.