At a bagel shop, 2 coffees and 4 bagels cost $6.00. Two coffees and 7 bagels cost $8.25. What is the unit price of one coffee and the unit price of one bagel?
2c + 4b = 600
2c + 7b = 825
subtract them:
3b = 225
b = 75
sub b = 75 back into the firs equation and solve for c
let me know what you get.
my answer:
1 bagel= $0.75
1 coffee= $1.00
To find the unit price of one coffee and one bagel, we need to set up a system of equations based on the given information.
Let's assume the unit price of one coffee is 'C' dollars and the unit price of one bagel is 'B' dollars.
From the first statement, "2 coffees and 4 bagels cost $6.00", we can write the equation:
2C + 4B = 6.00
From the second statement, "Two coffees and 7 bagels cost $8.25", we can write the equation:
2C + 7B = 8.25
Now, we have a system of equations:
2C + 4B = 6.00 ---(1)
2C + 7B = 8.25 ---(2)
To solve this system, we can use the method of elimination or substitution. Let's use the method of substitution.
First, solve equation (1) for C:
2C = 6 - 4B
C = (6 - 4B) / 2
C = 3 - 2B ---(3)
Now, substitute equation (3) into equation (2):
2(3 - 2B) + 7B = 8.25
6 - 4B + 7B = 8.25
3B = 2.25
B = 2.25 / 3
B = 0.75
Now that we have 'B' (the unit price of one bagel), we can substitute this value back into equation (3) to find 'C' (the unit price of one coffee):
C = 3 - 2(0.75)
C = 3 - 1.50
C = 1.50
Therefore, the unit price of one coffee is $1.50 and the unit price of one bagel is $0.75.