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.
let g be the price of green peppers and r be the price of red peppers.
3*g + 2*r = 3.45
4*g + 3*r = 5.00
Use algebra to solve for g and r
3*g+2*r=3.45
To find the price of each variety of pepper, we can set up a system of equations based on the given information.
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 first statement, Dave buys 3 green peppers and 2 red peppers for a total of $3.45. Hence, our first equation can be written as:
3x + 2y = 3.45 ---(1)
According to the second statement, Ruth buys 4 green peppers and 3 red peppers for a total of $5.00. Hence, our second equation can be written as:
4x + 3y = 5.00 ---(2)
To solve these equations and find the values of 'x' and 'y', we can use the method of elimination or substitution.
Let's solve using the method of substitution:
From Equation (1), we can express 3x as (3.45 - 2y) and substitute this value in Equation (2):
4(3.45 - 2y) + 3y = 5.00
Now, simplify and solve for 'y':
13.80 - 8y + 3y = 5.00
5y = 5.00 - 13.80
5y = -8.80
y = -8.80 / 5
y = -1.76
Now, let's substitute the value of 'y' (-1.76) into Equation (1) to find 'x':
3x + 2(-1.76) = 3.45
3x - 3.52 = 3.45
3x = 3.45 + 3.52
3x = 6.97
x = 6.97 / 3
x = 2.32
So, the price of each green pepper is $2.32, and the price of each red pepper is $1.76.