Question

Dani and Chris are the leaders of their school's kindness club. As a gift for the beginning of the year, they are going to buy one tote bag and one t-shirt for each member of the club. They are each doing internet research on the cost of the bags and the shirts. Here is some information you will need to know:

The club has $150 in the bank to spend on the gifts. There are 7 members of the club who will receive tote bags and t-shirts. When you write your expressions, use t to stand for the cost of each t-shirt. When you write your expressions, use b to stand for the cost of each tote bag.
1. Dani decides to add the cost of each shirt and the cost of each bag together, and then multiply by seven to find the total cost. Write an algebraic expression for the total cost of the gifts using Dani's method. Remember, use t and b as your variables.
2. Chris is going to multiply the cost of each shirt by seven and then multiply the cost of each bag by seven, and then add those two values together to find the total cost. Write an algebraic expression for the total cost of the gifts using Chris's method. Remember, use t and b as your variables.
3. Dani and Chris are arguing about which method will correctly calculate the cost of the gifts. You are asked to settle the argument. Is one method better than the other? Explain.
4. Dani and Chris decide to purchase a tote bag that costs $7.40 each and a t-shirt that costs $12.60 each. Calculate the total cost for all the gifts using both Dani's method and Chris's method. Can they afford to buy these gifts?
(Make sure to show your work and write your answer in the form of a sentence.)

Answer 1

1. Dani's method: 7(t + b). 2. Chris's method: 7t + 7b. 3. Both methods are valid. 4. Total cost using Dani's method: $140. Total cost using Chris's method: $140. They can afford the gifts.

Step-by-step explanation:

Dani's Method:

The algebraic expression for Dani's method to find the total cost of the gifts is 7(t + b). This expression adds the cost of each shirt and the cost of each bag together, and then multiplies by seven.

Chris's Method:

The algebraic expression for Chris's method to find the total cost of the gifts is 7t + 7b. This expression multiplies the cost of each shirt by seven, multiplies the cost of each bag by seven, and then adds those two values together.

Comparison:

Both methods result in calculating the total cost of the gifts. However, Dani's method adds the costs together before multiplying by seven, while Chris's method multiplies each cost by seven and then adds them together. Both methods will yield the same answer as long as the individual costs are not different. Therefore, one method is not better than the other as long as the individual costs are consistent.

Total Cost:

Given that the tote bags cost $7.40 each and the t-shirts cost $12.60 each, we can calculate the total cost using both methods.

Dani's Method: Total Cost = 7(12.60 + 7.40) = 7(20) = $140

Chris's Method: Total Cost = 7(12.60) + 7(7.40) = 88.20 + 51.80 = $140

They can afford to buy these gifts as the total cost of $140 is less than the $150 they have in the bank.