How do I set this problem up and solve it.
Mrs. Muniz's algebra class was collecting money for a party. The class decided that each student should give the same amount of money. They collected a total of $9.61. If everyone used 5 coins, how many nickels were collected
961 is only divisible evenly by 31, so 31 students must have given 31 cents each. (31 x 31 = 961)
The only way to make 31 cents with 5 coins is: one cent, two dimes and two nickels. Since its says everyone used 5 coins (which would be very unusual), there must have been a total of 31 x 2 = 62 nickels collected.
You can't do this problem with algebra. I is an exercise in mathematical logic. The key to the problem is to find the number that divides 961 evenly. There is only one such number, 31.
To set up and solve this problem, follow these steps:
1. Understand the problem: Read the problem carefully to identify the given information and what needs to be determined. In this case, we know that the class collected a total of $9.61 and that each student gave the same amount of money. The goal is to find out how many nickels were collected.
2. Determine the total number of students: Since each student gave the same amount of money, we can find the number of students by dividing the total amount collected ($9.61) by the value contributed by each student. In this case, the total amount collected should equal the number of students multiplied by the amount contributed by each student.
Let's assume the number of students is "x" and the amount contributed by each student is "a". So, we can set up the equation:
x * a = $9.61
3. Find the value contributed by each student: To determine the value contributed by each student, we need to find a number that evenly divides $9.61. In this case, it is stated in the problem that 961 is divisible only by 31. So, we can conclude that each student contributed 31 cents.
4. Determine the number of nickels: Since each student used 5 coins, and one of the coins is 1 cent, we need to decompose 31 cents using the remaining 4 coins.
The decomposition that fits 31 cents and uses 4 coins is: 2 dimes (20 cents), and 2 nickels (10 cents).
Therefore, out of the 31 cents contributed by each student, 10 cents came from nickels.
5. Calculate the total number of nickels collected: To find the total number of nickels collected, we multiply the number of students by the number of nickels each student contributed.
Since we determined that each student contributed 31 cents and 10 cents of that came from nickels, we can calculate the total number of nickels as follows:
Total number of nickels = Number of students * Number of nickels contributed by each student
= x * 2 nickels (since each student contributed 2 nickels)
However, since we established earlier that the number of students is equal to 31 (as 31 x 31 = 961), we can directly substitute 31 for x:
Total number of nickels = 31 * 2 nickels = 62 nickels
Therefore, a total of 62 nickels were collected by Mrs. Muniz's algebra class.