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
$0.10
$0.10
$2.50
$2.50
$0.70
$0.70
$2.80
Let's assume the cost of a 2-inch marble is x cents.
According to the information given, the cost of a 1-inch marble would be (x - 30) cents.
Rochelle buys 25 1-inch marbles for her science project, so the total cost of these marbles would be 25 * (x - 30) cents.
We also know that Rochelle spent exactly $10, which is equal to 1000 cents.
Therefore, we can set up the equation:
25 * (x - 30) = 1000
Simplifying, we get:
25x - 750 = 1000
Adding 750 to both sides of the equation:
25x = 1000 + 750
25x = 1750
Dividing both sides by 25:
x = 70
Thus, the cost of a 2-inch marble is $0.70.
Tickets to the baseball game are on sale for $1.50 off the regular price. Dea buys 6 tickets. If her total cost is $51, what is the regular price of each ticket? Write and solve an equation of the form p(x±q)=r . Then write a sentence to explain your answer.(4 points)
Let's assume the regular price of each ticket is x dollars.
Since Dea buys 6 tickets, her total cost would be 6x dollars.
According to the information given, she gets a discount of $1.50 off the regular price. So, the discounted price of each ticket would be x - $1.50.
Therefore, Dea's total cost can be represented as 6 * (x - $1.50) dollars.
We also know that her total cost is $51.
Setting up the equation:
6 * (x - $1.50) = $51
Simplifying, we get:
6x - (6 * $1.50) = $51
6x - $9 = $51
Adding $9 to both sides of the equation:
6x = $60
Dividing both sides by 6:
x = $10
Thus, the regular price of each ticket is $10.
Explanation:
We can set up the equation 6 * (x - $1.50) = $51 to represent Dea's total cost. By simplifying and solving this equation, we find that the regular price of each ticket is $10.