A candy machine contains 5 times the number of nickels in dimes and is less than 16 the number of quarters. Total value is $12.80. How many are there nickels and dimes?

I can't understand what means 5 times the number of nickels in dimes. How do you put nickels in dimes? How can this be re-worded so that it makes sense? Even then I don't think I'll know how to write the equation and solve it. Can someone help?

Sorry I remembered it wrong. Here it is again.

A candy machine contains 5 times the number of nickels in dimes and 16 less than the number of nickels in quarters. How many of each are there?

I understand your confusion. The phrase "5 times the number of nickels in dimes" is a bit ambiguous and might be reworded to make it clearer. One possible way to rephrase it could be "The number of nickels is 5 times the number of dimes."

To solve this problem, we can break it down into three equations:

Let's assume the number of nickels is represented by 'n,' the number of dimes by 'd,' and the number of quarters by 'q.'

1. The candy machine contains 5 times the number of nickels in dimes: This means that the number of nickels (n) is equal to 5 times the number of dimes (d). We can write this as: n = 5d.

2. The machine is less than 16 times the number of quarters: This means that the total number of coins in the machine is less than 16 times the number of quarters (q). Mathematically, this can be expressed as: n + d + q < 16q.

3. The total value in the candy machine is $12.80: We can convert the value of each coin and sum them up. The value of a nickel is $0.05, a dime is $0.10, and a quarter is $0.25. So, the equation for the total value can be written as: 0.05n + 0.10d + 0.25q = 12.80.

To solve this system of equations, we can use substitution or elimination. Let's substitute n in terms of d from the first equation into the second and third equations:

Substituting n = 5d into the second equation: 5d + d + q < 16q.
Simplifying this equation: 6d + q < 16q.

Substituting n = 5d into the third equation: 0.05(5d) + 0.10d + 0.25q = 12.80.
Simplifying this equation: 0.25d + 0.10d + 0.25q = 12.80.

Now, we have two equations:
6d + q < 16q
0.25d + 0.10d + 0.25q = 12.80.

By solving this system of equations, we can find the values of d (number of dimes) and n (number of nickels).

I hope this explanation helps you understand how to approach and solve the problem.