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suter [353]
3 years ago
15

I have 12 more nickels than quarters. If the coins are worth $5.40, how many nickels are there?

Mathematics
1 answer:
Ne4ueva [31]3 years ago
8 0

Let's try to create two equations to help us solve this problem. For this problem, n will represent the number of nickels and q will represent the number of quarters.


A first one could represent the number of <em>coins </em>we have. This does not regard the value of the coins, but rather just how many we could <em>count</em>. Based on the information in the problem, we could say:

n = 12 + q

After all, the number of nickels is 12 more than the number of quarters.


Now, let's create an equation to represent the value of the coins we have. Since each n nickel is worth 5 cents, we can say the value of all the nickels in cents is 5n. We can thus say for quarters that the value of all quarters in cents is 25q. Since we know the value of the coins we have adds to $5.40, or 540 cents, we can say:

5n + 25q = 540


Now, we have two equations:

n = 12 + q

5n + 25q = 540


We can use substitution to find our answers:

5(12 + q) + 25q = 540

60 + 5q + 25q = 540

30q + 60 = 540

30q = 480

q = 16


We have now found that the number of quarters we have is 16. When we use this value in one of our equations, we can find n:

n = 12 + q

n = 12 + 16 = 28


We have 16 quarters and 28 nickels.

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no we equate the derivative to zero and solve for x.

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