Karen buys 5 cups of coffee and 2 bagels for 26$. Kenneth buys 3 cups of coffee and 3 bagels for 21$ . How much does one cup of coffee cost? How much does one bagel cost?
5c + 2b = 26 (multiply by 3)
3c + 3b = 21 (multiply by 2)
15c + 6b = 78
6c + 6b = 42 (subtract)
9c = 36
After finding c, insert into one of the original equation to find b.
To find the cost of one cup of coffee and one bagel, we need to set up a system of equations based on the given information.
Let's assume the cost of one cup of coffee is represented by 'C' and the cost of one bagel is represented by 'B'.
Based on the information given, we can set up the following equations:
1. Karen buys 5 cups of coffee and 2 bagels for $26:
5C + 2B = 26
2. Kenneth buys 3 cups of coffee and 3 bagels for $21:
3C + 3B = 21
Now, we can solve this system of equations to determine the values of 'C' and 'B'.
To do this, we can use a method called substitution.
Step 1: Solve Equation 1 for C in terms of B:
5C = 26 - 2B
C = (26 - 2B)/5
Step 2: Substitute the value of C in Equation 2 with (26 - 2B)/5:
3[(26 - 2B)/5] + 3B = 21
Step 3: Simplify and solve for B:
(78 - 6B + 15B)/5 = 21
78 + 9B = 105
9B = 105 - 78
9B = 27
B = 27/9
B = 3
Now that we have the value of B, we can substitute it back into either Equation 1 or Equation 2 to find the value of C. Let's use Equation 1:
5C + 2(3) = 26
5C + 6 = 26
5C = 26 - 6
5C = 20
C = 20/5
C = 4
Therefore, one cup of coffee costs $4 and one bagel costs $3.