Solve using systems

Question

Jerry Rice, who played the majority of his career with the San Francisco 49ers and the Oakland Raiders, holds the all-time record for touchdown (TD) passes caught. Here are some interesting facts about this feat.

?He caught 30 more TD passes from Steve Young than he did from a Joe Montana.

?He caught 39 more TD passes from Joe Montana than he did from Rich Gannon.

?He caught a total of 156 TD passes from Young, Montana,  and Gannon.

Determine the number of touchdown passes Rice has caught from Young, from Montana, and from Gannon.

Answer 1

The first equation represents catches from Young and Montana: Y = M + 30.

The second equation represents catches from Montana and Gannon: M = G + 39.

The last equation represents total TD catches: Y + M + G = 156.

Solve the second equation for G: G = M - 39.

Now you can use substititution to rewrite the last equation as (M + 30) + M + (M - 39) = 156.

Solve that equation for M and use that solution to determine Y and G.