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.
I need help with some of the problems I have all ready posted please help me
use a matrix
To solve this problem, we need to set up a system of equations.
Let's assume the price of a green pepper is represented by the variable 'g', and the price of a red pepper is represented by the variable 'r'.
Based on the information given, we can set up the following equations:
Equation 1: 3g + 2r = 3.45 (Dave's purchase)
Equation 2: 4g + 3r = 5.00 (Ruth's purchase)
To find the price of each variety of pepper, we can solve this system of equations using the method of substitution or elimination.
Let's use the method of elimination:
Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of 'r' the same:
Equation 1: 9g + 6r = 10.35
Equation 2: 8g + 6r = 10.00
Now, subtract Equation 2 from Equation 1 to eliminate 'r':
(9g + 6r) - (8g + 6r) = 10.35 - 10.00
g = 0.35
So the price of a green pepper is $0.35.
Substitute this value back into Equation 1 to solve for 'r':
3(0.35) + 2r = 3.45
1.05 + 2r = 3.45
2r = 3.45 - 1.05
2r = 2.40
r = 2.40 / 2
r = 1.20
Therefore, the price of a red pepper is $1.20.
In conclusion, the price of each variety of pepper is $0.35 for a green pepper and $1.20 for a red pepper.