Question

5 bags and 6 pens together cost 226 dollars whereas 4 bags and 3 pens together cost 305 dollars. Find the cost of a bag and a pen (Correct to two decimal places)

Answer 1

The cost of a bag is $128 and the cost of a pen is $-69.

Step-by-step explanation:

Let's create a system of equations to solve this problem. Let's represent the cost of a bag as 'b' and the cost of a pen as 'p'.

1. First equation: 5b + 6p = 226
2. Second equation: 4b + 3p = 305

Now we can solve this system of equations. By multiplying the first equation by 4 and the second equation by 5, we can eliminate 'b' and solve for 'p'.

Multiplying the equations: 20b + 24p = 904 and 20b + 15p = 1525. By subtracting the second equation from the first equation, we get 9p = -621. Dividing by 9, we find that p = -69.

Substituting the value of p into one of the original equations, we can solve for 'b'. Let's use the first equation: 5b + 6(-69) = 226. Simplifying, we get 5b - 414 = 226. Adding 414 to both sides, we get 5b = 640. Dividing by 5, we find that b = 128.

Therefore, the cost of a bag is $128 and the cost of a pen is $-69.

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