Question

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 will be \( x - 0.30 \) dollars (since it costs 30 cents less).

Rochelle buys 25 1-inch marbles for a total of $10. Thus, we can write the equation:

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

Now, simplify the equation:

\[ 25x - 7.50 = 10 \]

Next, add 7.50 to both sides:

\[ 25x = 17.50 \]

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

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

So the cost of a 2-inch marble is \( \mathbf{0.70} \) dollars.

The answer is $0.70.