Question

A company sells trinkets and doodads. A small grab bag contains 2 trinkets and 1 doodad and sells for $7. A large grab bag contains 5 trinkets and 3 doodads and sells for $19. How much do trinkets and doodads sell for individually? (Assume no mark-up on the grab bags.)

A. Trinkets cost $2 and doodads cost $3.
B. Trinkets cost $2.00 and doodads cost $5.00.
C. Trinkets cost $3 and doodads cost $2.
D. Trinkets cost $1.70 and doodads cost $3.50.

Answer 1

By setting up and solving a system of equations, it is determined that trinkets cost $2 each and doodads cost $3 each. The price of each item was found by using two equations derived from the cost of small and large grab bags.

Step-by-step explanation:

To solve the problem of determining the individual price of trinkets and doodads, we can set up a system of equations based on the information provided:

• A small grab bag (2 trinkets + 1 doodad = $7)
• A large grab bag (5 trinkets + 3 doodads = $19)

Let's denote the price of a trinket as T and the price of a doodad as D. Now we have two equations:

1. 2T + D = 7 (1)
2. 5T + 3D = 19 (2)

Multiplying equation (1) by 3, we get:

6T + 3D = 21 (3)

Now, subtracting equation (2) from equation (3), we get:

6T + 3D - (5T + 3D) = 21 - 19

Which simplifies to:

T = 2

Substituting T = 2 back into equation (1), we get:

4 + D = 7

So:

D = 3

Therefore, trinkets cost $2 each and doodads cost $3 each, which corresponds to option A.