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

$2.80
$2.80

$0.10
$0.10

$2.50
$2.50

$0.70.

Answer 1

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

Rochelle buys 25 1-inch marbles and spends exactly $10. Therefore, we can write the equation:

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

Now, let's solve for \( x \):

1. Simplify the left side of the equation:

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

2. Distribute the 25:

\[ 25x - 7.50 = 10 \]

3. Add 7.50 to both sides:

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

4. Divide both sides by 25:

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

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