Question

rob and charlie have 36 coins that are nickels and dimes. if the value of the coins is $3.00, how many more dimes than nickels do they have ?

Answer 1

Rob and Charlie have 12 more dimes than nickels.

Step-by-step explanation:

To find the number of dimes and nickels, you can set up a system of equations based on the information given. Let's say rob has x number of nickels and charlie has y number of dimes. Since rob and charlie have a total of 36 coins, we know that x + y = 36. Since the value of the coins is $3.00, we can set up another equation based on the value of nickels (0.05x) and dimes (0.10y): 0.05x + 0.10y = 3.00.

To solve the system of equations, we can multiply the first equation by 0.05 to make the coefficients of x match: 0.05x + 0.05y = 1.80. Subtracting this equation from the second equation gives us: 0.10y - 0.05y = 3.00 - 1.80. Simplifying further, 0.05y = 1.20. Dividing both sides by 0.05 gives us y = 24, which represents the number of dimes. Plugging this value back into the first equation gives us x + 24 = 36. Subtracting 24 from both sides gives us x = 12, which represents the number of nickels.

To find the difference between the number of dimes and nickels, we can subtract the value of x from y: 24 - 12 = 12. Therefore, rob and charlie have 12 more dimes than nickels.

Answer 2

Rob and Charlie have 12 more dimes than nickels.

Step-by-step explanation:

Translate the problem into equations: Let x be the number of nickels and y be the number of dimes. We know:

Total number of coins: x + y = 36

Total value of coins: 0.05x + 0.1y = 3.00 (since nickels are worth $0.05 and dimes are worth $0.1)

Solve the system of equations: We can solve the first equation for y: y = 36 - x. Substitute this into the second equation:

0.05x + 0.1(36 - x) = 3.00

Simplify and solve for x: 0.05x + 3.6 - 0.1x = 3.00

0.05x = 0.6

x = 12

Find the number of dimes: Substitute x back into the equation for y:

y = 36 - 12 = 24

Calculate the difference: The number of additional dimes is y - x = 24 - 12 = 12.

Therefore, Rob and Charlie have 12 more dimes than nickels.