Question

6 paul has 40 coins, all dimes and quarters, worth $7.60. how many dimes and how many quarters does he have? let d represent the number of dimes and q represent the number of quarters.
(a) set a system of equations.
equation 1:
equation 2:
(b) paul has dimes and quarters.

Explanation:

Step1: Total coins equation

$d + q = 40$

Step2: Total value equation

$0.10d + 0.25q = 7.60$

Step3: Isolate $d$ from Step1

$d = 40 - q$

Step4: Substitute $d$ into Step2

$0.10(40 - q) + 0.25q = 7.60$

Step5: Simplify and solve for $q$

$4 - 0.10q + 0.25q = 7.60$
$0.15q = 3.60$
$q = \frac{3.60}{0.15} = 24$

Step6: Solve for $d$ using $q=24$

$d = 40 - 24 = 16$

Answer:

(a)

Equation 1: $d + q = 40$
Equation 2: $0.10d + 0.25q = 7.60$

(b)

Paul has 16 dimes and 24 quarters.