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) Responses $2.50 $2.50 $0.70 $0.70 $0.10 $0.10 $2.80

1 answer

Let the cost of a 2-inch marble be \( x \) dollars. Then, the cost of a 1-inch marble is \( x - 0.30 \) dollars.

Rochelle buys 25 1-inch marbles for a total cost of $10. We can set up the equation based on this information:

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

Now, simplify the equation:

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

\[ 25x - 7.50 = 10 \]

Add 7.50 to both sides:

\[ 25x = 10 + 7.50 \]

\[ 25x = 17.50 \]

Now, divide both sides by 25 to find \( x \):

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

Thus, the cost of a 2-inch marble is \( \boxed{0.70} \) dollars.