Question

Can someone help me please I’m struggling

Miss Hassan needs supplies for her classroom. She buys 4 calculators and 7 protractors for
a total cost of $48.20. A week later, she buys 5 more of the same calculator and 2 more of the
same protractor for a total cost of $48.10. She now has 9 new calculators and 9 new protractors
to add to her supplies."
What is the cost of each item?

Answer 1

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.