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.

$0.10, $0.70, $2.80, $2.50

1 answer

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

Rochelle buys 25 1-inch marbles and spends a total of $10, which is equivalent to 1000 cents. Therefore, we can set up the equation for the total cost of the 1-inch marbles:

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

Now, let's simplify and solve for \( x \):

\[ 25x - 750 = 1000 \]

Adding 750 to both sides:

\[ 25x = 1750 \]

Now, divide by 25:

\[ x = 70 \]

Thus, the cost of a 2-inch marble is \( x = 70 \) cents.

Now let's verify:

The cost of a 1-inch marble would be:

\[ x - 30 = 70 - 30 = 40 \text{ cents} \]

The total cost for 25 1-inch marbles is:

\[ 25 \times 40 = 1000 \text{ cents} = 10 \text{ dollars} \]

This is consistent with the information provided. Therefore, the cost of a 2-inch marble is:

\[ \boxed{0.70} \]