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

$0.10
$2.80
$0.70
$2.50

1 answer

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

Rochelle buys 25 1 inch marbles, and the total cost for these marbles is given as $10, which is equivalent to 1000 cents. Thus, we can set up the following equation:

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

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

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

Dividing both sides by 25:

\[ x - 30 = 40 \]

Adding 30 to both sides gives:

\[ x = 70 \]

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

Thus, the answer is:

\[ \boxed{0.70} \]