At one store, a trophy costs $12.50 and engraving costs $0.40 per letter. at another store, the same trophy costs $14.75 and engraving costs $0.25 per letter. how many letters must be engraved for the costs for this trophy at both stores to be the same?

When p is the number of letters being engraved:
12.5 + .4p = 14.75 + .25p
-12.5             -12.5
.4p = 2.25 + .25p
-.25p          -.25p
.15p = 2.25
/.15     /.15
p = 15
There would need to be 15 letters engraved for the cost of the trophies to be the same. Hope this helps!