You have a stack of pennies without counting the pennies, how can you know if there is a odd or even number of them

Let the number of two-hour lessons be x and the number of one-hour lessons be y; this gives us the equations
2x + y = 25
50x + 30y = 690
To find x and y, we can solve the quadratic equation provided;
from the first equation:
y = 25 - 2x.......i
By substituting equation i into the second equation, we arrive at:
50x + 30(25 - 2x) = 690
50x + 750 - 60x = 690
-10x = -60
So,
x = 6
Thus, we find that the total number of two-hour lessons is 6 hours.

I estimate that it would be about an hour and 15 minutes, but I'm not entirely sure.

Answer:

The solution to this problem indicates that Hernry invested $18,000 in stocks and $6,000 in bonds.

Step-by-step explanation:

First, you need to multiply 6 by 3. The outcome is 18, meaning it is three times higher than the bond amount. Next, subtract $24,000 from $18,000, which gives you $6,000, representing the bond investment. Hence, it is three times less than the stocks as the question describes.

Let’s define the number of nickels as n,

the number of dimes as d, and

the number of quarters as q.

The total quantity of coins is 844.

We can express this as "number of nickels + number of dimes + number of quarters = Total coins.

Thus, we can form an equation from this statement as

n+d+q = 844            ---------------------equation(1).

Additionally, it is given that Emilia possesses as many quarters as dimes.

Consequently, the number of quarters equals the number of dimes.

This leads to another equation:

q = d                          ------------------------equation(2).

It is also stated that there are "twice as many nickels as dimes."

We can create a further equation representing this statement as

n = two times the number of dimes

or n= 2d                -------------------------- equation (3).

Three equations have been established.

Let’s solve this system of three equations using substitution methods.

By substituting q = d and  n= 2d  into equation (1), we obtain

n+d+q = 844      =>

2d +d + d = 844.

Adding up the d's, gives us

4d =844.

Dividing both sides by 4 yields

d = 211.

Hence, the quantity of dimes = 211.

Next, we will determine the number of nickels and quarters.

We know that the number of quarters equals the number of dimes.

Thus, the total count of quarters is 211.

The overall quantity of coins sums to 844.

Hence, the number of nickels = 844 -  (sum of quarters and dimes).= 844 -(211+211) = 844 - 422

= 422.

Therefore,

the total of nickels = 422.

Now, let’s compute the total values of all coins.

A nickel is valued at $0.05

A dime is valued at $0.10

A quarter is valued at $0.25.

The total value = 0.05 *(number of nickels) + 0.10*(number of dimes) + 0.25*(number of quarters).

=[ 0.05* 422 + 0.10 *211 + 0.25*211].

= 21.10 + 21.10 + 52.75.

= 94.95.

So, the total worth of all 844 coins = $94.95.

Emilia saved $94.95.