Charles has a collection of dimes and quarters worth $1.25. he has 8 coins. write a systems of equations to represent this situation. then solve the system to determine how many dimes and how many quarters charles has.
step by step pls

* The systems of equations are:

# d + q = 8 ⇒ (1)

# 10d + 25q = 125 ⇒ (2)

Charles has 5 dimes and 3 quarters

Step-by-step explanation:

* Lets explain how to solve the problem

- Charles has a collection of dimes and quarters worth $1.25

- He has 8 coins

* To solve the problem remember that:

# 1 dim = 10 cents

# 1 quarter = 25 cents

# 1 dollar = 100 cents

- Assume that the number of dimes is d and the number of

 quarter is q

∵ Charles has 8 coins

- The number of dimes and the number of quarters equal the

  number of the coins

∴ d + q = 8 ⇒ (1)

∵ 1 dime = 10 cents

∴ The value of dimes = 10 × d = 10d

∵ 1 quarter = 25 cents

∴ The value of quarters = 25 × q = 25q

∵ The collection worth $1.25

∵ 1 dollar = 100 cents

∴ The collection worth = 1.25 × 100 = 125 cents

∴ 10d + 25q = 125 ⇒ (2)

* The systems of equations are:

# d + q = 8 ⇒ (1)

# 10d + 25q = 125 ⇒ (2)

* Lets solve the equations

- Multiply equation (1) by (-10) to eliminate d

∴ -10d + -10q = -80 ⇒ (3)

- Add equations (2) and (3)

∴ 15q = 45

- Divide both sides by 15

∴ q = 3

- Substitute the value of q in equation (1) to find the value of d

∴ d + 3 = 8

- Subtract 3 from both sides

∴ d = 5

∵ d represents the number of dimes and q represents the number

  of quarters

∴ Charles has 5 dimes and 3 quarters

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following