At one store a trophy costs 12.50 dollars and engraving cost 0.40 cents. At another store the same trophy costs 14.75 dollar and engraving costs 0.25 cents. How many letters, e must be engraved for the costs to be the same?

15 letters

What will the cost of e, letters?
18.5

Thanks!

To find the number of letters e that must be engraved for the costs to be the same, we need to set up an equation and solve for e.

Let's assume that x is the number of letters to be engraved.

At the first store, the total cost is $12.50 + $0.40x = 12.50 + 0.40x.

At the second store, the total cost is $14.75 + $0.25x = 14.75 + 0.25x.

Setting these two costs equal, we get the equation:
12.50 + 0.40x = 14.75 + 0.25x.

Simplifying the equation, we have:
0.40x - 0.25x = 14.75 - 12.50,
0.15x = 2.25.

Dividing both sides of the equation by 0.15, we find:
x = 2.25 / 0.15,
x = 15.

Therefore, the number of letters e that must be engraved for the costs to be the same is 15.

To find the cost of e letters, we can substitute the value of e into one of the equations. Let's use the first store equation:

Cost = $12.50 + $0.40(e).
Cost = $12.50 + $0.40(15).
Cost = $12.50 + $6.
Cost = $18.50.

Therefore, the cost of engraving 15 letters is $18.50.

To determine the number of letters, e, that must be engraved for the costs to be the same, we need to set up an equation.

Let's start with the first store. The total cost at the first store is the cost of the trophy ($12.50) plus the cost of engraving ($0.40) per letter, so it can be represented as:

Total cost at first store = $12.50 + $0.40e

Similarly, for the second store, the total cost is the cost of the trophy ($14.75) plus the cost of engraving ($0.25) per letter, so it can be represented as:

Total cost at second store = $14.75 + $0.25e

Now, to find out how many letters, e, must be engraved for the costs to be the same, we can set up an equation:

$12.50 + $0.40e = $14.75 + $0.25e

To solve for e, we can rearrange the equation:

$0.40e - $0.25e = $14.75 - $12.50

$0.15e = $2.25

Dividing both sides by $0.15:

e = $2.25 / $0.15

e = 15

Therefore, 15 letters must be engraved for the costs to be the same.

To find the cost of engraving e letters, we can substitute e = 15 into the equation:

Cost of engraving 15 letters = $0.25 * 15

Cost of engraving 15 letters = $3.75

Therefore, the cost of engraving 15 letters is $3.75.