Question

Odette solved this problem:

A piggy bank has nickels and dimes totaling $1.15. If the bank contains exactly 15 coins, how many of each coin are in the bank?
In Odette's solution, 7 is the number of:
A. Dimes.
B. Quarters.
C. Pennies.
D. Halves.

Answer 1

To solve this problem, you can use algebra and create a system of equations. By substituting or eliminating variables, you can find the values for n (number of nickels) and d (number of dimes). In this particular case, there are 7 nickels and 8 dimes in the piggy bank.

Step-by-step explanation:

To solve this problem, let's use algebra. Let n represent the number of nickels and d represent the number of dimes.

We're given two pieces of information:

1. The total value of nickels and dimes is $1.15, which can be expressed as 5n + 10d = 115 (because a nickel is worth 5 cents and a dime is worth 10 cents).
2. The total number of coins is 15, so we have n + d = 15 (because n represents the number of nickels and d represents the number of dimes).

We have a system of two equations:

1. 5n + 10d = 115
2. n + d = 15

We can solve this system of equations by substitution or elimination.

Let's use elimination:

1. Multiply the second equation by 5 to make the coefficients of n in both equations equal: 5(n + d) = 5(15) = 75.
2. Subtract the second equation from the first equation: (5n + 10d) - (5n + 5d) = 115 - 75 => 5d = 40.
3. Divide both sides of the equation by 5 to solve for d: d = 40/5 = 8.
4. Substitute the value of d back into the second equation to solve for n: n + 8 = 15 => n = 15 - 8 = 7.

Therefore, there are 7 nickels and 8 dimes in the piggy bank.