Answer: cost of a bagel $1.25, cost of a muffin $1.75
Step-by-step 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 }
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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