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?
Let x = # of nickels, y = # of dimes
x + y = 42
y = 42 - x
5x + 10y = 385
Substitute 42 - x for y.
5x + 10(42-x) = 385
Solve for x.
a peggy 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 peggy
a 17-foot ladder leans against a wall. if the ladder is 8 feet from the base of the wall, how far is it from the bottom of the wall to the top of the ladder
10-foot ladder leans against an 8-foot wall. How far from the wall should the foot of the ladder be placed so that the top of the ladder will be exactly at the top of the wall?
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the number of nickels in the piggy bank is "n," and the number of dimes is "d."
We know that the total number of coins is 42, so we can write the equation:
n + d = 42
We also know that the total value of the coins is $3.85, which can be expressed in cents as 385 cents. Since a nickel is worth 5 cents and a dime is worth 10 cents, the equation for the value can be written as:
5n + 10d = 385
Now we have a system of two equations:
n + d = 42
5n + 10d = 385
To solve this system, we can use the method of substitution or elimination.
Let's start with the method of substitution. Solve the first equation for n in terms of d:
n = 42 - d
Substitute this expression for n in the second equation:
5(42 - d) + 10d = 385
Now, simplify and solve for d:
210 - 5d + 10d = 385
5d = 385 - 210
5d = 175
d = 35
Now that we have the value for d (number of dimes), substitute it into the first equation to find n:
n + 35 = 42
n = 42 - 35
n = 7
Therefore, there are 7 nickels in the piggy bank.