A Wonsan has 30 coins in her pocket, all of which are dimes and quarters . If the total value of the coins is $4.50 ,how many dimes and how many quarters does she have ?

The number of

Dimes = d = 20 dimes

Quarters = q = 10 quarters

Step-by-step explanation:

Let us represent

The number of :

Dimes = d

Quarters = q

Note that:

A dime is worth 10 cents = 0.10d

A quarter is worth 25 cents = 0.25q

A Wonsan has 30 coins in her pocket, all of which are dimes and quarters .

d + q = 30 Equation 1

d = 30 - q

If the total value of the coins is $4.50

0.10d + 0.25 q = 4.50Equation 2

We substitute 30 - q for d in Equation 2

0.10(30 - q) + 0.25q = 4.50

3 - 0.10q + 0.25q = 4.50

- 0.10q + 0.25q = 4.50 - 3

0.15q = 1.5

q = 1.5/0.15

q = 10 quarters

Solving for d

d = 30 - q

d = 30 - 10

d = 20 dimes

Therefore:

The number of

Dimes = d = 20 dimes

Quarters = q = 10 quarters

23

step-by-step explanation: