Question

At one store a trophy costs $12. Engraving costs $0.20 per letter. At another store, the same trophy costs $18. Engraving costs $0.10. How many letters, e, must be engraved for the costs to be the same?

Answer 1

To find the number of letters that must be engraved for the costs to be the same at two different stores, set up an equation for the total cost at each store and solve for the number of letters. The calculations show that 60 letters must be engraved for the costs to be equal.

Step-by-step explanation:

The student is asking to calculate the number of letters, e, that need to be engraved on a trophy for the cost to be the same at two different stores. To find this, we can set up an equation representing the total cost at each store and solve for e.

Let's denote the cost of engraving per letter at the first store as $0.20, and the cost of the trophy as $12. Therefore, the total cost at the first store for e letters engraved would be: Cost1 = $12 + $0.20e.

At the second store, the cost of the trophy is $18, and the engraving cost per letter is $0.10. The total cost at the second store for e letters engraved would then be: Cost2 = $18 + $0.10e.

For the costs to be equal, Cost1 = Cost2. Plugging in the expressions for each cost we get:

$12 + $0.20e = $18 + $0.10e

Subtract $0.10e from both sides and $12 from both sides gives us:

$0.10e = $6

Dividing both sides by $0.10, we find that e equals:

e = 60

Thus, 60 letters must be engraved on the trophy for the costs at both stores to be the same.