Question

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?

Answer 1

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.

Answer 2

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!