Answer:
* The systems of equations are:
# d + q = 8 ⇒ (1)
# 10d + 25q = 125 ⇒ (2)
Charles has 5 dimes and 3 quarters
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