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