00:01
This problem, we're told that a bag contains 200 total coins, combined with, or combined of, quarters, dimes, and nickels.
00:07
Now we know that the bag has a total value of $20.
00:10
The last piece of information they tell us is that there's four times as many dimes as quarters.
00:15
We want to know how many of each of the coins is in the bag.
00:18
Well, in this case, we have three different coins.
00:20
We have our quarters, dimes, and nickels.
00:22
So i'm going to have q represent the number of quarters, d will represent the number of dimes, and n will represent a number of nickels.
00:30
Well, the first piece of information they tell us is there's 200 total coins.
00:34
So when we add up the number of quarters, the number of d, and the number of nickels, which we're calling q, d and n, that should equal to 200.
00:40
So that's how we get our first equation.
00:42
The number of quarters, which is q, plus the number of dimes, which is d, plus the number of nickels, which is n, should equal the total number of coins, which is 200.
00:51
Now, the second big piece of information they tell us is the total value of all of our coins.
00:56
Well, in this case, we know that a quarter is 25 cents.
01:00
So if we take 25 cents and multiply it by the number of quarters we have, that will be the total number of quarters in the bag, or the total value of all the quarters in the bag.
01:09
Well, dimes are worth 10 cents.
01:11
So if we take 10 cents and multiply it by the number of dimes in the bag, which is d, that will represent the total value of all the d.
01:18
And then for the nickels, those are worth five cents.
01:20
So if we take five cents and multiply it by the number of nickels, which is n, that should equal the total value.
01:25
Of the nickels.
01:27
So when we add all of these together, that should equal to the total amount of money, which is $20.
01:32
And lastly, we know that we have four times as many dimes as quarters, which means that we have more dimes than we have quarters.
01:40
So we can write an equation to represent the number of dimes.
01:43
The number of dimes is four times the number of quarters, because there's four times as many dimes as quarters.
01:49
Perfect.
01:50
So now we have three variables and three equations.
01:53
So we can go ahead and solve? well, i'm going to use substitution because we know that d is equal to four times q.
01:58
So i'm going to substitute 4q in place of d in our first two equations.
02:03
So that's going to give us q plus 4q plus n equal to 200.
02:09
And for the second equation, that's going to be 0 .25q plus 0 .10 times 4q plus our 0 .05n equals 20...