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.

Question

Responses

$0.10

$0.70

$2.50

$2.80

Answer 1

To find the cost of a 2-inch marble, let's denote the cost of a 2-inch marble as \( x \) (in dollars). Since the 1-inch marbles cost 30 cents less, the cost of a 1-inch marble would be \( x - 0.30 \).

Rochelle buys 25 1-inch marbles for a total of $10, which gives the equation:

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

Now, we can simplify this equation:

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

Dividing both sides by 25:

\[ x - 0.30 = \frac{10}{25} \]

\[ x - 0.30 = 0.40 \]

Now, to find the value of \( x \), we add 0.30 to both sides:

\[ x = 0.40 + 0.30 \]

\[ x = 0.70 \]

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