There are three times as many robins as cardinals visited a bird feeder. If a total of 20 robins and cardinals visited the feeder, how many were robins? Must solve using a systems.
To solve this problem using a system of equations, we need to set up two equations based on the given information.
Let's assume the number of cardinals visiting the bird feeder is represented by the variable 'c', and the number of robins is represented by the variable 'r'.
From the given information, we have two pieces of information:
1) The number of robins is three times the number of cardinals: r = 3c.
2) The total number of robins and cardinals is 20: r + c = 20.
Now we have a system of two equations:
r = 3c (Equation 1)
r + c = 20 (Equation 2)
To solve this system, we can use the method of substitution or elimination. Let's use the substitution method here.
Substitute the value of r from Equation 1 into Equation 2:
3c + c = 20
4c = 20
c = 20/4
c = 5
Now, substitute the value of c back into Equation 1 to find the value of r:
r = 3(5)
r = 15
Therefore, there were 15 robins that visited the bird feeder.
Let's solve this problem using a system of equations.
Let's use "R" to represent the number of robins and "C" to represent the number of cardinals.
Given that there are three times as many robins as cardinals, we can write the equation:
R = 3C (equation 1)
Also, the total number of robins and cardinals that visited the feeder is 20, so:
R + C = 20 (equation 2)
Now let's solve this system of equations.
Substitute equation 1 into equation 2:
3C + C = 20
Combine like terms:
4C = 20
Divide both sides by 4:
C = 20/4
C = 5
Now substitute the value of C into equation 1:
R = 3(5)
R = 15
Therefore, there were 15 robins that visited the bird feeder.
r + c = 20
r = 3c
personally, I would not use two variables for a simple one like this
No. of cardinals = x
then robbins = 3x
x + 3x = 20
so easy .... this way