Question

devont had a handful of dimes and quarters in his pocket. he counted 41 coins and realized they were worth $7.55. write and solve a system of linear equations to determine the number of dimes and quarters devont had.

Explanation:

Step1: Define variables

Let $d$ = number of dimes, $q$ = number of quarters.

Step2: Set up total coins equation

Total coins: $d + q = 41$

Step3: Set up total value equation

Value in dollars: $0.10d + 0.25q = 7.55$

Step4: Solve for one variable

From Step2: $d = 41 - q$

Step5: Substitute into value equation

$$0.10(41 - q) + 0.25q = 7.55$$
$$4.10 - 0.10q + 0.25q = 7.55$$
$$4.10 + 0.15q = 7.55$$

Step6: Isolate q term

$$0.15q = 7.55 - 4.10$$
$$0.15q = 3.45$$

Step7: Solve for q

$$q = \frac{3.45}{0.15} = 23$$

Step8: Solve for d

$$d = 41 - 23 = 18$$

Answer:

Devont had 18 dimes and 23 quarters.