How would you solve this problem??
A piggy bank contains only nickels and dimes. In all there are 42 coins with a total value of $3.85. How many nickels are in the piggy bank??
two equations
: n+d=42
.05n+.10d=3.85 or 5n+10d=385
Sorry forgot to post the answers, which one would it be??
And can you show how you solved it??
A-3
B-7
C-17
D-35
Thanks
Ok I got it. Its process of elimination. So it would be B-7.
To solve this problem, we need to set up a system of equations based on the given information. Let's use variables to represent the number of nickels and dimes in the piggy bank.
Let's say the number of nickels is represented by 'n', and the number of dimes is represented by 'd'.
1. The first equation is based on the total number of coins in the piggy bank:
n + d = 42
2. The second equation is based on the total value of the coins in the piggy bank:
0.05n + 0.10d = 3.85
Now we have a system of equations to solve. We can use the substitution method or the elimination method to find the values of 'n' and 'd'.
Let's use the substitution method:
1. Solve the first equation for 'n': n = 42 - d.
2. Substitute this expression for 'n' in the second equation:
0.05(42 - d) + 0.10d = 3.85.
Simplify the equation:
2.10 - 0.05d + 0.10d = 3.85.
Combine like terms:
0.05d = 1.75.
Divide both sides by 0.05 to isolate 'd':
d = 35.
Now substitute the value of 'd' back into the first equation to find 'n':
n + 35 = 42.
Subtract 35 from both sides:
n = 7.
Therefore, there are 7 nickels in the piggy bank.