Writing Linear Systems from Word Problems

A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than the number of songs that the drummer wrote. They wrote a total of 46 songs.

Which system of equations models this situation if the drummer wrote d songs and the guitarist wrote g songs?

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  The doughnuts were more popular than the coffee, so on Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. 

Which system of equations could be used to represent this situation? 

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed.

Which system of equations could be used to represent this situation?

Derek mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins, and the total came to $6.60. 

Which system of equations could be used to find the exact number of dimes and nickels? 

Stefan's school is selling tickets to a musical performance. On the first day of sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets.

Which equations represents the system that could be used?

A large pizza at Palanzio’s Pizzeria costs $6.80 plus 90 cents for each topping. The cost of a large pizza at Guido’s Pizza is $7.30 plus 65 cents for each topping. 

Which system of equations could be used to find the number of toppings when both companies cost the same amount?