Question

the wild dogs sell t - shirts and hats at their games. last season, they sold 152 total items. hats cost $8.50 each and t - shirts cost $12. if their total revenue was $1,656, how many of each item did the wild dogs sell? what is true of the system of equations that represents this scenario? check all that apply. one equation represents the total number of items sold using the price of each item as a rate. one equation represents the total number of items sold, equaling the sum of the variables. one equation represents the total revenue using the price of each item as a rate. one variable represents the total games and the other represents the total number of items sold. one variable represents the total hats sold and the other represents the total t - shirts sold.

Explanation:

1. Let \( h \) be the number of hats and \( t \) be the number of t - shirts. The total number of items sold is \( h + t=152 \), so one equation represents the total number of items sold as the sum of the variables (hats and t - shirts), so the option "One equation represents the total number of items sold, equaling the sum of the variables" is correct.
2. The total revenue is \( 8.5h + 12t = 1656 \), where the price of each hat (\( \$8.50 \)) and each t - shirt (\( \$12 \)) are used as rates to calculate the total revenue, so the option "One equation represents the total revenue using the price of each item as a rate" is correct.
3. The variables \( h \) and \( t \) represent the number of hats and t - shirts sold respectively, so the option "One variable represents the total hats sold and the other represents the total t - shirts sold" is correct.
4. The equation for the total number of items sold (\( h + t = 152 \)) does not use the price of each item as a rate, so the option "One equation represents the total number of items sold using the price of each item as a rate" is incorrect.
5. The variables do not represent the total games and the total number of items sold (they represent hats and t - shirts), so the option "One variable represents the total games and the other represents the total number of items sold" is incorrect.

Answer:

• One equation represents the total number of items sold, equaling the sum of the variables.
• One equation represents the total revenue using the price of each item as a rate.
• One variable represents the total hats sold and the other represents the total t - shirts sold.