Jenna always throws loose change into a pencil holder on desk and takes it out every 2 weeks. this time it is all nickels and dimes. There are 7 times as many dimes as nickels and the value of the dimes is $6.50 more than the value of the nickels. How many dimes does Jenna have?

Question

Jenna always throws loose change into a pencil holder on desk and takes it out every 2 weeks. this time it is all nickels and dimes. There are 7 times as many dimes as nickels and the value of the dimes is $6.50 more than the value of the nickels. How many dimes does Jenna have?

Answer 1

d = 7n

10d = 650+5n

10(7n) = 650+5n
65n = 650
n=10
so, d=70

Answer 2

Let's assume the number of nickels Jenna has as "n" and the number of dimes as "d".

According to the given information, there are 7 times as many dimes as nickels, so we can write an equation as:

d = 7n (Equation 1)

The value of the dimes is $6.50 more than the value of the nickels. The value of a single dime is 10 cents and the value of a single nickel is 5 cents.

We can write another equation based on the values of the dimes and nickels as:

0.10d = 0.05n + 6.50 (Equation 2)

To solve this system of equations, we can substitute Equation 1 into Equation 2.

0.10(7n) = 0.05n + 6.50
0.70n = 0.05n + 6.50
(0.70n - 0.05n) = 6.50
0.65n = 6.50
n = 6.50 / 0.65
n = 10

Now we can substitute the value of n back into Equation 1 to find the value of d:

d = 7(10)
d = 70

Therefore, Jenna has 70 dimes.

Answer 3

To solve this problem, we can set up a system of equations based on the given information.

Let's assume the number of nickels Jenna has is represented by 'n', and the number of dimes she has is represented by 'd'.

From the given information, we know:
1. There are 7 times as many dimes as nickels: d = 7n

Now, let's calculate the value of the nickels and dimes:
2. Value of nickels = 5 cents * number of nickels = 5n cents
3. Value of dimes = 10 cents * number of dimes = 10d cents

We are also given that the value of the dimes is $6.50 more than the value of the nickels:
4. Value of dimes = Value of nickels + $6.50
10d = 5n + 650

Now, we can substitute the value of 'd' from equation 1 into equation 4:
10(7n) = 5n + 650
70n = 5n + 650
65n = 650
n = 10

Now, we know the number of nickels is 10. We can substitute this value into equation 1 to find the number of dimes:
d = 7n
d = 7*10
d = 70

Therefore, Jenna has 70 dimes.