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If 6 pens and 7 pencils together cost Rs.90, while 5 pens and 6 pencils cost Rs.76, what will be the cost of each pen?

Question

If 6 pens and 7 pencils together cost Rs.90, while 5 pens and 6 pencils cost Rs.76, what will be the cost of each pen?

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Solution

Let's solve this problem step by step:

Step 1: Let's denote the cost of a pen as P and the cost of a pencil as Q.

Step 2: From the problem, we can form two equations based on the given information. The first equation is from the first sentence: 6P + 7Q = 90. The second equation is from the second sentence: 5P + 6Q = 76.

Step 3: Now, we have a system of two equations, and we can solve it using substitution or elimination method. Let's use the elimination method. Multiply the first equation by 5 and the second equation by 6, we get: 30P + 35Q = 450 and 30P + 36Q = 456.

Step 4: Subtract the second equation from the first, we get: -Q = -6, or Q = 6.

Step 5: Substitute Q = 6 into the first equation, we get: 6P + 7*6 = 90, or 6P = 90 - 42 = 48, or P = 48 / 6 = 8.

So, the cost of each pen is Rs.8.

This problem has been solved

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