Marbles come in two sizes: 1-inch diameter and 2-inch diameter. The 1-inch diameter marbles cost 30 cents less than the 2-inch marbles. Rochelle buys 25 1-inch marbles for her science project and spends exactly $10. Find the cost of a 2-inch marble.(1 point)

Question

Responses

$2.80
$2.80

$0.70
$0.70

$0.10
$0.10

$2.50
$2.50

Answer 1

Let the cost of a 2-inch marble be \( x \) cents. Then, the cost of a 1-inch marble would be \( x - 30 \) cents.

Rochelle buys 25 1-inch marbles and spends exactly $10, which is 1000 cents. Therefore, we can set up the following equation based on the total cost:

\[ 25(x - 30) = 1000 \]

Now, let's solve this equation:

1. Distribute the 25:

\[ 25x - 750 = 1000 \]

2. Add 750 to both sides:

\[ 25x = 1750 \]

3. Divide by 25:

\[ x = 70 \]

This means the cost of a 2-inch marble is \( x = 70 \) cents or \( $0.70 \).

Thus, the cost of a 2-inch marble is:

\[ \boxed{0.70} \]