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

$2.80
$2.50
$0.70
$0.10

Answer 1

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 bought 25 1-inch marbles for a total cost of $10, so we can set up the following equation:

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

Now, simplify the equation:

\[ 25x - 25 \times 0.30 = 10 \] \[ 25x - 7.5 = 10 \]

Next, add 7.5 to both sides:

\[ 25x = 10 + 7.5 \] \[ 25x = 17.5 \]

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

\[ x = \frac{17.5}{25} = 0.70 \]

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