Question

In her closet, Andrea has 3 times as many sweaters as she has button-up shirts. The sweaters cost $20 each, and the button-up shirts cost $12. If the total amount that she paid for button-up shirts and sweaters was $288, which system of equations can be used to determine the number of sweaters (S) and button-up shirts (B) that she owns?

a) S = 3B
20S + 12B = 288

b) S = 12B
20S + 3B = 288

c) S = B/3
20S + 12B = 288

d) S = B
20S + 20B = 288

Answer 1

The correct system of equations is: (a) S = 3B and 20S + 12B = 288. The first equation represents the relationship between sweaters and shirts, while the second equation accounts for the total cost of both items.

Step-by-step explanation:

The question to solve is: If Andrea has 3 times as many sweaters as she has button-up shirts, and the total amount she paid for button-up shirts and sweaters was $288, which system of equations can be used to determine the number of sweaters (S) and button-up shirts (B) that she owns?

Firstly, we can represent the number of sweaters as 3 times the number of button-up shirts, giving us the equation S = 3B. This represents the relationship between the number of sweaters (S) and button-up shirts (B).

Next, we know that each sweater costs $20 and each button-up shirt costs $12. Since the total cost is $288, we can set up the second equation based on the cost of the sweaters and shirts: 20S + 12B = 288.

Thus, the correct system of equations to determine the number of sweaters and button-up shirts Andrea owns is:

• S = 3B
• 20S + 12B = 288

So, the answer is (a) S = 3B and 20S + 12B = 288.

Answer 2

The correct system of equations to determine the number of sweaters (S) and button-up shirts (B) that Andrea owns is option (a), S = 3B and 20S + 12B = 288.

Step-by-step explanation:

To determine the number of sweaters (S) and button-up shirts (B) that Andrea owns, we need to set up a system of equations based on the given information. The first part of the information tells us that Andrea has 3 times as many sweaters as she has button-up shirts, which can be written as an equation: S = 3B. The second part of the information mentions that the total amount paid for both sweaters and buttons-ups is $288. Since sweaters cost $20 each and button-up shirts cost $12 each, we can express this as another equation: 20S + 12B = 288.

Combining these two equations, we obtain the following system of equations which we can use to solve for S and B:

1. S = 3B
2. 20S + 12B = 288

Therefore, the correct system of equations is represented by option (a).