## Answer :

*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!

**Answer : The number of letters engraved on each trophy must be 15.**

**Step-by-step explanation :**

As we are given,

A trophy cost at one store = $ 12.50

Engraving cost per letter at one store = $ 0.40 × L

where, 'L' is number of letters.

A trophy cost at another store = $ 14.75

Engraving cost per letter at another store = $ 0.25 × L

**Now we have to determine the number of letters must be engraved for the costs for this trophy at both stores to be the same.**

$ 12.50 + ($ 0.40 × L) = $ 14.75 + ($ 0.25 × L)

($ 0.40 × L) - ($ 0.25 × L) = $ 14.75 - $ 12.50

$ 0.15 × L = $ 2.25

L = ($ 2.25) ÷ ($ 0.15)

**L = 15**

**Therefore, the number of letters engraved on each trophy must be 15.**