Dave buys 3 green peppers and 2 red peppers for $3.45. Ruth buys 4 green peppers and 3 red peppers for $ 5.00. Find the price of each variety of pepper.
This is one of those problems where you have to set up the peppers as variables. Lets say green peppers are "x" and red peppers are "y".
You can then make up a systems of equations to solve for each variable.
Dave:
3x + 2y = 3.45
and
Ruth:
4x + 3y = 5.00
Now in order to solve each other you can use two techniques: one is to eliminate one term and solve for the other, or do substitution method.
I'm going to do the first one:
Now you can either cancel the "x" or "y" term. I'll choose "x"
Now in order to cancel, they have to be equal, but also one of them has to be a negative value.
So:
4(3x+2y) = 4(3.45)
-3(4x+3y) = -3(5.00)
If you add each up you'd get:
12x+8y = 13.8
-12x-9y = -15
Which would end up being:
-y = -1.2
So y = $1.2
Now you can plug "y" back into any equation.
I'll pick Dave's:
3x + 2(1.2) = 3.45
So 3x + 2.4 = 3.45
3x = 1.05
x = $0.35
Now since we said x is green and y is red:
Green Peppers are 35 cents, and Red Peppers are 1.2 dollars.
In order to check, you can sub the x and y into Ruth's equation.
To find the price of each variety of pepper, let's assume the price of a green pepper is "x" dollars and the price of a red pepper is "y" dollars.
According to the given information, we can form two equations:
Equation 1:
3x + 2y = 3.45 (Dave's purchase)
Equation 2:
4x + 3y = 5.00 (Ruth's purchase)
We now have a system of two equations with two variables. We can solve this system using either substitution or elimination method.
Let's use the elimination method in this case.
Multiply Equation 1 by 4 and Equation 2 by 3 to eliminate the variable "x":
Equation 1:
4(3x + 2y) = 4(3.45)
12x + 8y = 13.80
Equation 2:
3(4x + 3y) = 3(5.00)
12x + 9y = 15.00
Now, subtract Equation 2 from Equation 1 to eliminate "x":
(12x + 8y) - (12x + 9y) = 13.80 - 15.00
12x - 12x + 8y - 9y = -1.20
-y = -1.20
y = 1.20
Now substitute the value of "y" into Equation 1 or 2 to find the value of "x":
3x + 2(1.20) = 3.45
3x + 2.40 = 3.45
3x = 3.45 - 2.40
3x = 1.05
x = 1.05 / 3
x = 0.35
Therefore, the price of a green pepper is $0.35 and the price of a red pepper is $1.20.