Robert bought 3 bagels and 2 muffins at a bakery for $7.25. karen bought 5 bagels and 4 muffins for $13.25. what is the cost of each item?

cost of a bagel $1.25, cost of a muffin $1.75

Explanation

By translating the word information to algebraic language you obtain two equations with two unknowns, which form a system of equations which can be solved to obtain the cost of each item.

1) Name the variables:

b: number of bagels
m: number of muffins

2) Translate the word statements into algebraic equations:

2.1) Robert bought 3 bagels and 2 muffins for $ 7.25

=> 3b + 2m = $7.25 equation (1)

2.2) Karen bought 5 bagels and 4 muffins for $ 13.25

=> 5b + 4m = 13.25 equation (2)

3) Set the sysmen

3b+2m = 7.25
5b + 4m = 13.25

4) Mutilply the first equation by 2:

6b + 4m = 14.5

5) Subtract the second equation from previous result:

       6b + 4m = 14.5
-   {(5b + 4m) = 13.25 }

     6b - 5b = 14.50 - 13.25

      b         =  1.25

6) Replace the value of b in the any of the original equations:

3(1.25) + 2m = 7.25

=> 3.75 + 2m = 7.25
=> 2m = 7.25 - 3.75
=> 2m = 3.50
=> m = 3.50 / 2 = 1.75

Solution: b = $1.25, m = $1.75.

7) Verfify the solution:

3 bagles and 2 muffins for $ 7.25 =>

3(1.25) + 2(1.75) = 7.25

3.75 + 3.50 = 7.25

 7.25 = 7.25 => check

5 bagels and 4 muffins for $13.25

5(1.25) + 4(1.75) = 13.25

6.25 + 7 = 13.25

13.25 = 13.25 => check