Question

Maria wants to buy a trophy and engrave her son's name on it. At Trophies Unlimited, trophies cost $12 each, and engraving costs 40¢ per letter, while at Centerpiece Trophies, trophies are $12.50 each, and engraving is 30¢ per letter. If Maria's costs would be the same at both stores, which equation shows the number of letters, x, in her son's name?

A) 12(x + 0.4) = 12.5(x + 0.3)
B) 12 + 0.4x = 12.5 + 0.3x
C) 0.4 + 12x = 0.3 + 12.5x
D) 12 + 0.4x = 12.5 - 0.3x

Answer 1

The correct equation to represent the number of letters, x, in her son's name when the costs would be the same at both Trophies Unlimited and Centerpiece Trophies is $12 + $0.40x = $12.50 + $0.30x.

Step-by-step explanation:

To help Maria determine which equation shows the number of letters, x, in her son's name when the costs would be the same at both stores, we need to set up an equation that represents the total cost of each store and then equate them.

At Trophies Unlimited, the cost of the trophy is $12, and engraving costs $0.40 per letter. So for x letters, the total cost at Trophies Unlimited is $12 + $0.40x.

At Centerpiece Trophies, the trophy is $12.50 each, and engraving costs $0.30 per letter. Thus, for x letters, the total cost at Centerpiece Trophies is $12.50 + $0.30x.

Setting these two expressions equal to each other, we get the equation:
$12 + $0.40x = $12.50 + $0.30x. This matches option B.