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

$0.70
$0.70

$2.50
$2.50

$0.10
$0.10

$2.80
$2.80

Answer 1

Let the cost of a 2-inch marble be \( x \) dollars. Since the 1-inch marbles cost 30 cents less than the 2-inch marbles, the cost of a 1-inch marble would be \( x - 0.30 \) dollars.

Rochelle buys 25 1-inch marbles for a total of $10. Therefore, we can set up the following equation:

\[ 25 \times (x - 0.30) = 10 \]

Now, simplify and solve for \( x \):

\[ 25x - 7.50 = 10 \]

Adding \( 7.50 \) to both sides gives:

\[ 25x = 17.50 \]

Now, divide by 25:

\[ x = \frac{17.50}{25} = 0.70 \]

So, the cost of a 2-inch marble is \( 0.70 \) dollars, or 70 cents.

Thus, the answer is:

$0.70