Question

Toby's piggy bank contains only 5c and 10c coins. If it contains 65 coins with a total value of 3.80, find the number of each type of coin.

Let x and y be the number of 5c and 10c coins respectively.
1a
Use the fact that the total number of coins is 65 to set up Equation 1.
Write the equation in the form ax+by=c, where a is positive.

Answer 1

Toby's piggy bank contains 54 5c coins and 11 10c coins. This was determined by setting up and solving a system of equations based on the total number of coins and their total value.

Step-by-step explanation:

To solve for the number of 5c and 10c coins in Toby's piggy bank, we will set up a system of equations using the variables x for the number of 5c coins and y for the number of 10c coins. Since we know there are a total of 65 coins, we can write the first equation as:

Equation 1: x + y = 65

This equation represents the total number of coins. Now, we'll use the total value of all the coins, $3.80, to set up the second equation. The value equation is:

Equation 2: 0.05x + 0.10y = 3.80

We have two equations with two unknowns:

1. x + y = 65
2. 0.05x + 0.10y = 3.80

To solve this system of equations, we can use substitution or elimination method. If we multiply the second equation by 20 to eliminate the decimals, we get:

Equation 3: x + 2y = 76

Now, subtract Equation 1 from Equation 3 and solve for y:

y = 76 - 65 = 11

Substitute y = 11 back into Equation 1 to find x:

x = 65 - 11 = 54

Therefore, there are 54 5c coins and 11 10c coins in Toby's piggy bank.