Question

At a clothing store, T-shirts cost $20, and shirts cost $25. If the store wants to sell at least $600 worth of T-shirts and shirts, write and solve the inequality representing the situation.

Answer 1

To sell at least $600 worth of T-shirts and shirts, where T-shirts cost $20 and shirts cost $25, we use the inequality 20T + 25S ≥ 600. The variables T and S represent the number of T-shirts and shirts sold, respectively. This inequality has infinitely many solutions without additional constraints on T and S.

Step-by-step explanation:

To represent the situation of selling at least $600 worth of T-shirts and shirts at a clothing store where T-shirts cost $20 and shirts cost $25, we need to write an inequality. Let's define T as the number of T-shirts sold and S as the number of shirts sold.

Using the given prices, the inequality to represent the total sales (T-shirt sales plus shirt sales) being at least $600 is:

20T + 25S ≥ 600

To solve the inequality, we can graph the inequality on a coordinate plane, choose test points, or use algebraic methods like substitution or elimination if we have constraints for the number of T-shirts or shirts sold.

Without additional constraints, there are infinitely many solutions to this inequality - combinations of T and S that will ensure the sales are at least $600. For example, if the store sells 10 T-shirts (T=10), they need to sell at least 16 shirts (S=16) to meet the target because 20(10) + 25(16) = 200 + 400 = 600.