Question

At one store a trophy scosts $12.50. Engraving costs $0.40 per letter. At another store, the same trophy costs $14.75. Engraving Costs $0.25. How many letters, e, must be engraved for the costs to be the same?

Answer 1

The number of letters that need to be engraved for the costs to be the same at both stores is 15.

Step-by-step explanation:

To determine how many letters need to be engraved for the costs to be the same at two different stores, we need to set up and solve an equation. Let's call the number of letters to be engraved e.

At one store, the cost of the trophy is $12.50 and the engraving costs $0.40 per letter. So the total cost at this store would be $12.50 + $0.40e.

At another store, the trophy costs $14.75 and the engraving costs $0.25 per letter. The total cost at this store would be $14.75 + $0.25e.

To find the number of letters that makes the costs equal, we set the two total costs equal to each other:

12.50 + 0.40e = 14.75 + 0.25e

Now we solve for e:

1. Subtract 0.25e from both sides of the equation: 0.40e - 0.25e = 14.75 - 12.50
2. Simplify both sides: 0.15e = 2.25
3. Divide both sides by 0.15: e = 2.25 / 0.15
4. Calculate the result: e = 15

Therefore, 15 letters need to be engraved for the costs at both stores to be the same.