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

$0.70
$0.70

$0.10
$0.10

$2.80
$2.80

$2.50
$2.50

Answer 1

Let the cost of a 2-inch marble be \( x \) cents.

According to the problem, the cost of a 1-inch marble is \( x - 30 \) cents.

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

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

Expanding this gives:

\[ 25x - 750 = 1000 \]

Adding 750 to both sides results in:

\[ 25x = 1750 \]

Now, divide by 25:

\[ x = \frac{1750}{25} = 70 \]

So the cost of a 2-inch marble is \( 70 \) cents, which is:

\[ \text{$0.70} \]

Thus, the cost of a 2-inch marble is $0.70.