Let [tex]x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_{10}, x_{11}[/tex] be the weight of i-th player.
1. If the mean weight of 4 backfield members on the football team is 221 lb, then
[tex]\dfrac{x_1+x_2+x_3+x_4}{4}=221\ lb.[/tex]
2. If the mean weight of the 7 other players is 202 lb, then
[tex]\dfrac{x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}}{7}=202\ lb.[/tex]
3. From the previous statements you have that
[tex]x_1+x_2+x_3+x_4=221\cdot 4=884 \lb,\\ \\x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}=202\cdot 7=1414\ lb.[/tex]
Add these two equalities and then divide by 11:
[tex]x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}=884+1414=2298\ lb,\\ \\\dfrac{x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}}{11}=\dfrac{2298}{11}=208\dfrac{10}{11}\ lb.[/tex]
Answer: the mean weight of the 11-person team is [tex]208\dfrac{10}{11}\ lb.[/tex]
