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

Responses

$0.10
$0.10

$2.50
$2.50

$0.70
$0.70

$2.80...

Answer 1

Let's denote the cost of a 2-inch marble as \( x \) (in dollars). Consequently, the cost of the 1-inch marbles would be \( x - 0.30 \).

Rochelle buys 25 1-inch marbles for her science project and spends a total of $10. Therefore, we can set up the following equation:

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

Now, let's simplify the equation:

\[ 25x - 25 \times 0.30 = 10 \] \[ 25x - 7.50 = 10 \]

Next, we add 7.50 to both sides of the equation:

\[ 25x = 10 + 7.50 \] \[ 25x = 17.50 \]

Now, divide both sides by 25:

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

Thus, the cost of a 2-inch marble is \( x = 0.70 \) dollars, or 70 cents.

The answer is:

$0.70