Question

Jackie has a collection of stamps and coins. The total number of stamps and coins is 81. The number of coins is one more than three times the number of stamps. Find out how many stamps and coins Jackie has. Part A: Write let statements that represent the variables in this situation (2 points) Part B: Set up a system of equations that you can use to solve this problem? (2 points) Part C: Solve the system from (b) by using either substitution or elimination *show all solving steps*. (4 points) Part D: Write a solution statement answering the question

Answer 1

Jackie collected 61 coins and 20 stamps

Explanation:

Solving (a): Variable representation

Let the coins be represented with c

Let the stamps be represented with s

Solving (b): Setup equation

Total is 81. This implies that:

`s + c = 81`

Also:

`c = 1 + 3s`

Solving (c): Solve the system

Substitute 1 + 3s for c in
`s + c = 81`

`s + 1 + 3s = 81`

Collect Like Terms

`s + 3s = 81-1`

`4s= 80`

Divide both sides by 4

`s = (80)/(4)`

`s= 20`

Substitute 20 for s in
`c = 1 + 3s`

`c = 1 + 3 * 20`

`c = 1 + 60`

`c = 61`

Solving (d): Solution statement

Jackie collected 61 coins and 20 stamps