Carrie has 27 coins in her purse. All the coins are 5 cent or 20 cent
coins. If the total value of the coins is $3.75, how many of each type
does she have?
Let x = number of 5 cent coins
and y = number of 20 cent coind
----------------------------------
x + y = 27
5x + 20y = 375
---------------------
Solve the two equations simultaneously. If you want to put it in just one equation it will be
5x + 20(27-x) = 375 and solve for x.
start with a lot of 20-cent coins
18x20 + 3x5 = 375
That makes 21 coins. Each 20-cent coin that you replace with four 5-cent coins will add 3 coins to the count.
See where this is going?
The working out has to be in algebraic form
Well, clearly Carrie has quite a lot of coins in her purse. Maybe she should invest in a wallet instead! Now, let's try to solve this puzzle. Let's start by assuming that Carrie has x 5 cent coins and y 20 cent coins.
Mathematically, we can form two equations based on the given information:
1) x + y = 27 (since Carrie has a total of 27 coins)
2) 0.05x + 0.20y = 3.75 (since the total value of the coins is $3.75, with 5 cent coins worth $0.05 and 20 cent coins worth $0.20)
Now, let's put on our mathematical clown shoes and solve this set of equations:
From the first equation, we can express x in terms of y as:
x = 27 - y
Substituting this value of x into the second equation, we get:
0.05(27 - y) + 0.20y = 3.75
Now, let's simplify this equation:
1.35 - 0.05y + 0.20y = 3.75
0.15y = 2.4
Dividing both sides by 0.15, we find that y = 16.
Substituting this value of y back into the first equation, we get:
x + 16 = 27
x = 11
So, Carrie has 11 coins worth 5 cents and 16 coins worth 20 cents.
I hope Carrie didn't lose her mind while counting all those coins!
To solve this problem, we can set up a system of equations. Let's use the variables x and y to represent the number of 5 cent and 20 cent coins, respectively.
We know that Carrie has a total of 27 coins, so we can write the equation:
x + y = 27 --------------(1)
We also know that the total value of the coins is $3.75, which can be written as:
0.05x + 0.20y = 3.75 --------------(2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method:
From equation (1), we can express x in terms of y as:
x = 27 - y
Now, substitute this value of x into equation (2):
0.05(27 - y) + 0.20y = 3.75
Simplify and solve for y:
1.35 - 0.05y + 0.20y = 3.75
0.15y = 2.40
y = 2.40 / 0.15
y = 16
Now that we have the value of y, we can substitute it into equation (1) to find the value of x:
x + 16 = 27
x = 27 - 16
x = 11
So, Carrie has 11 five cent coins and 16 twenty cent coins.