Anne has 20 coins in her pocket consisting of nickels and dimes only. The total value of the coins is $1.45. How many nickels and how many dimes does she have? (Let x represent the number of nickels and y represent the number of dimes.)
d represents Dimes
n represents Nickles
Total number of coins;
d + n = 20, n = (20-d) ...1
Total value of coins;
10d + 5n = 145 ...2
substitute equation 2 with equation 1 for n,
10d + 5(20-d) = 145,
10d + 100 - 5d =145,
10d -5d = 145 -100, d = 45/5 = 9 dimes
20 - 9 = 11 nickles
wrong
Let's use a system of equations to solve the problem.
1. The total number of coins is given as 20:
x + y = 20 (Equation 1)
2. The total value of the coins is given as $1.45:
0.05x + 0.10y = 1.45 (Equation 2)
To solve this system of equations, we can use substitution or elimination method. Let's use substitution.
1. Solve Equation 1 for x:
x = 20 - y
2. Substitute the value of x in Equation 2:
0.05(20 - y) + 0.10y = 1.45
Expanding the equation:
1 - 0.05y + 0.10y = 1.45
Simplifying the equation:
0.05y = 1.45 - 1
0.05y = 0.45
Divide both sides by 0.05:
y = 0.45 / 0.05
y = 9
3. Substitute the value of y in Equation 1:
x + 9 = 20
Subtract 9 from both sides:
x = 20 - 9
x = 11
Therefore, Anne has 11 nickels and 9 dimes.
To solve this problem, we need to set up a system of equations based on the given information.
Let's start by representing the number of nickels and dimes with variables:
Let x be the number of nickels.
Let y be the number of dimes.
We are given two pieces of information:
1) Anne has 20 coins in total, so the equation for the total number of coins is:
x + y = 20
2) The value of the coins in Anne's pocket is $1.45, so the equation for the total value of the coins is:
0.05x + 0.10y = 1.45
Now we have a system of two equations:
x + y = 20
0.05x + 0.10y = 1.45
We can solve this system of equations using substitution or elimination. Let's use the substitution method.
We'll solve the first equation for x:
x = 20 - y
Substitute this value of x into the second equation:
0.05(20 - y) + 0.10y = 1.45
Now we can solve for y:
1 - 0.05y + 0.10y = 1.45
0.05y + 0.10y = 1.45 - 1
0.15y = 0.45
y = 0.45 / 0.15
y = 3
Now that we have the value of y, we can substitute it back into the first equation to find x:
x + 3 = 20
x = 20 - 3
x = 17
Therefore, Anne has 17 nickels (x = 17) and 3 dimes (y = 3).