Marbles come in two sizes: 1 inch diameter and 2 inch diameter. The 1 inch diameter marbles cost 30 cents less than the 2ip inch marbles. Rochelle buys 25 1 inch marbles for her science project and spends exactly $10. Find the cost of a 2 I ch marble.

Question

$0.10
$2.80
$0.70
$2.50

Answer 1

Let the cost of a 2 inch marble be $x$ cents. Therefore, the cost of a 1 inch marble would be $x-30$ cents.

Rochelle buys 25 1 inch marbles, and the total cost for these marbles is given as $10, which is equivalent to 1000 cents. Thus, we can set up the following equation:

$$25\times (x-30)=1000$$

Now, simplify and solve for $x$:

$$25(x-30)=1000$$

Dividing both sides by 25:

$$x-30=40$$

Adding 30 to both sides gives:

$$x=70$$

Therefore, the cost of a 2 inch marble is $70$ cents or $0.70$ dollars.

Thus, the answer is:

$$\boxed{{\displaystyle 0.70}}$$