Question

Jamal has some quarters and dimes. He has 32 coins worth a total of $5.15. How many of each type of coin does he have?

a. Quarters: 13, Dimes: 19
b. Quarters: 17, Dimes: 15
c. Quarters: 20, Dimes: 12
d. Quarters: 15, Dimes: 17

Answer 1

To find the number of quarters and dimes Jamal has, we set up a system of equations and solved it to find out that Jamal has 13 quarters and 19 dimes.

Step-by-step explanation:

To solve the problem of how many quarters and dimes Jamal has, we need to set up a system of equations based on the information given: Jamal has 32 coins worth a total of $5.15. Let's assume the number of quarters is Q and the number of dimes is D. Since each quarter is worth $0.25 and each dime is worth $0.10, we can write two equations from the data provided:

• Q + D = 32 (Equation 1: Total number of coins)
• 0.25Q + 0.10D = 5.15 (Equation 2: Total value of coins in dollars)

Solving this system of equations will give us the exact number of quarters and dimes Jamal has. Multiplying Equation 2 by 100 to convert dollars into cents for easier calculations, we get:

• 25Q + 10D = 515

We can use substitution or elimination to solve these equations. If we multiply Equation 1 by 10, we get:

• 10Q + 10D = 320

Subtracting this from the new form of Equation 2 (25Q + 10D = 515) gives us:

• 15Q = 195, or Q = 195/15
• Q = 13

Substituting Q = 13 into Equation 1, we get:

• 13 + D = 32
• D = 32 - 13
• D = 19

So Jamal has 13 quarters and 19 dimes. The correct answer is a. Quarters: 13, Dimes: 19.