MATH SOLVE

3 months ago

Q:
# 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

Accepted Solution

A:

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