There are 4 times as many nickels as dimes in a coin bag. The coins have a total value of 600 cents ($6.00). Find the number of nickels. Write and solve an equation to do so.
(i found the answer through guess and check but i need to know the equation....btw the answer is 80 nickels and 20 dimes....plz help me find the equation)
Let n be the number of nickels
d the number of dimes
n = 4d because we are told "4 times as many nickels as dimes"
The total value is:
n * 5 + d * 10 = 600
Divide across by 5:
n + 2d = 120
and n=4d, so
4d + 2d = 120
6d = 120
d= 20
So n = 4d = 80
To find the equation, let's start by assigning variables to the quantities mentioned in the problem. Let's say the number of dimes is represented by "d" and the number of nickels is represented by "n".
We are given two pieces of information: first, that there are four times as many nickels as dimes, so we can write the equation n = 4d. Secondly, we know that the total value of the coins is 600 cents or $6.00, which can be written as 10d + 5n = 600.
Now we have a system of two equations:
n = 4d (equation 1)
10d + 5n = 600 (equation 2)
To solve this system, we can substitute equation 1 into equation 2 by replacing n with 4d:
10d + 5(4d) = 600
Simplifying:
10d + 20d = 600
30d = 600
Dividing both sides of the equation by 30:
d = 20
Now that we have the value for d (dimes), we can substitute it back into equation 1 to find the value of n (nickels):
n = 4(20) = 80
Therefore, there are 80 nickels and 20 dimes in the coin bag.