everyday when lisa returns from school she puts her change from buying lunch into a jar on her hair dresser. this weekend she decided to count her savings. she found that she had 72 coins all nickels and dimes. the total amount was $4.95. how many coins of each kind did she have ?
To solve this problem, we can set up a system of equations to represent the given information.
Let's assume Lisa has x number of nickels and y number of dimes.
According to the problem, we know that:
1. x + y = 72 (equation 1) - this represents the total number of coins she has.
2. 0.05x + 0.10y = 4.95 (equation 2) - this represents the total value of the coins she has.
Now we can solve this system of equations to find the values of x and y.
First, we can multiply equation 1 by 0.05 to match the coefficients of x:
0.05x + 0.05y = 3.60 (equation 3)
Next, we can subtract equation 3 from equation 2 to eliminate the x term:
(0.05x + 0.10y) - (0.05x + 0.05y) = 4.95 - 3.60
Simplifying:
0.10y - 0.05y = 1.35
0.05y = 1.35
y = 1.35 / 0.05
y = 27
Substitute the value of y (27) back into equation 1:
x + 27 = 72
x = 72 - 27
x = 45
Therefore, Lisa has 45 nickels (x) and 27 dimes (y).
n + d = 72
5n + 10 d = 495