Question

Tee shirts are sold for $15 each, and striped shirts are sold for $22 each. A total of 62 shirts are sold, and the total value of the shirts is $1098. What equation models this situation, and how many of each kind of shirt were sold?

A) Equation: 15x + 22y = 1098; Tee shirts sold: x, Striped shirts sold: y.
B) Equation: 22x + 15y = 1098; Tee shirts sold: x, Striped shirts sold: y.
C) Equation: 15x + 22y = 62; Tee shirts sold: x, Striped shirts sold: y.
D) Equation: 22x + 15y = 62; Tee shirts sold: x, Striped shirts sold: y.

Answer 1

The situation is modeled by two equations: x + y = 62 (total shirts) and 15x + 22y = 1098 (total value). Option A provides the correct equations to represent this situation, and by solving these equations, we can find the number of each type of shirt sold.

Step-by-step explanation:

The situation described in the student's question involves solving a system of linear equations representing the sale of two types of shirts: tee shirts and striped shirts. To determine how many of each type were sold, we need to set up two equations based on the given information:

1. The total number of shirts sold is 62.
2. The total value of the shirts sold is $1098.

Let's define x to be the number of tee shirts sold and y to be the number of striped shirts sold. The first equation comes from the total number of shirts: x + y = 62. The second equation uses the pricing information to represent the total value: 15x + 22y = 1098.

We can now consider the options provided:

• Option A is correct because it matches the equations we have derived from the given information.
• The other options are incorrect because they either mismatch the prices with the types of shirts or confuse the number of shirts sold with the total value of the shirts.

The correct model for this situation is represented by the equation 15x + 22y = 1098 and the total number of shirts sold by x + y = 62.