Michaela has $0.80 in nickels and dimes in her change purse. She has seven more nickels than dimes. How many coins of each type does she have?
just add up the coins and their values.
5n+10d = 80
n = d+5
Now just solve for n and d
10 nickels, 3 dimes
To solve this problem, we can set up a system of equations.
Let's represent the number of nickels as x and the number of dimes as y.
We know that the value of a nickel is $0.05 and the value of a dime is $0.10.
The total value of the coins is $0.80, so we can write the equation:
0.05x + 0.10y = 0.80
We also know that Michaela has seven more nickels than dimes. So the second equation is:
x = y + 7
Now we can use these equations to solve for the values of x and y.
To eliminate decimals, we can multiply both sides of the first equation by 100:
5x + 10y = 80
Now we have the system of equations:
5x + 10y = 80
x = y + 7
We can solve this system of equations using various methods such as substitution or elimination.
Let's solve it using substitution:
Substitute the value of x from the second equation into the first equation:
5(y + 7) + 10y = 80
5y + 35 + 10y = 80
15y + 35 = 80
15y = 45
y = 3
Now substitute this value of y back into the second equation to find the value of x:
x = 3 + 7
x = 10
Therefore, Michaela has 10 nickels and 3 dimes.