Answer: each calculator costs $6.77 and each protractor costs $7.13.
Step-by-step explanation:
Based on the information provided, we can use algebra to determine the cost of each item. Let x be the cost of one calculator and y be the cost of one protractor.
From the first purchase, we know that 4x + 7y = 48.20.
From the second purchase, we know that 5x + 2y = 48.10.
We can use these two equations to solve for x and y.
Multiplying the second equation by 2 and subtracting it from the first equation multiplied by 7, we get:
(28x + 49y) - (10x + 4y) = 48.20(7) - 48.10(2)
Simplifying, we get:
18x + 45y = 337.80
Dividing both sides by 9, we get:
2x + 5y = 37.53
Now, we can use the second equation to solve for x:
5x + 2y = 48.10
Rearranging, we get:
5x = 48.10 - 2y
Substituting this into the previous equation, we get:
2(48.10 - 2y) + 5y = 37.53
Simplifying, we get:
96.20 - 4y + 5y = 37.53
y = 7.13
Now that we know y, we can use either equation to solve for x:
5x + 2(7.13) = 48.10
5x = 33.84
x = 6.77
Therefore, each calculator costs $6.77 and each protractor costs $7.13.