Answer:
15 letters must be engraved for the cost to be the same.
Step-by-step explanation:
Let x represent number of letters.
We have been given that at a store a trophy cost $12.50. Engraving cost &0.40 per letter. So cost of engraving x letters at store one would be [tex]C_1=0.40x+12.50...(1)[/tex].
We are also told that at a other store the same trophy cost $14.75. Engraving cost $0.25. So cost of engraving x letters at store two would be [tex]C_2=0.25x+14.75...(2)[/tex].
To find the number of letters that must be engraved for the cost to be the same, we will equate both equations and solve for x.
[tex]0.40x+12.50=0.25x+14.75[/tex]
Combine like terms:
[tex]0.40x-0.25x=14.75-12.50[/tex]
[tex]0.15x=2.25[/tex]
[tex]\frac{0.15x}{0.15}=\frac{2.25}{0.15}[/tex]
[tex]x=15[/tex]
Therefore, 15 letters must be engraved for the cost to be the same.
