Washington Horton
09/21/2024 · Elementary School
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 3 doodads and sells for \( \$ 19 \). How much do trinkets and doodads sell for individually? (Assume no mark-up on the grab bags.) Trinkets cost \( \$ 3 \) and doodads cost \( \$ 2 \).
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find the individual prices of trinkets and doodads, we can set up a system of equations based on the information given about the grab bags.
Let:
- \( t \) = price of a trinket
- \( d \) = price of a doodad
From the problem, we have the following two equations based on the contents and prices of the grab bags:
1. For the small grab bag:
\[
2t + 1d = 7
\]
2. For the large grab bag:
\[
5t + 3d = 19
\]
Now we can solve this system of equations.
**Step 1: Solve the first equation for \( d \)**
From the first equation:
\[
d = 7 - 2t
\]
**Step 2: Substitute \( d \) into the second equation**
Substituting \( d \) into the second equation:
\[
5t + 3(7 - 2t) = 19
\]
Expanding this:
\[
5t + 21 - 6t = 19
\]
Combining like terms:
\[
-t + 21 = 19
\]
**Step 3: Solve for \( t \)**
Subtracting 21 from both sides:
\[
-t = 19 - 21
\]
\[
-t = -2
\]
\[
t = 2
\]
**Step 4: Substitute \( t \) back to find \( d \)**
Now substitute \( t = 2 \) back into the equation for \( d \):
\[
d = 7 - 2(2)
\]
\[
d = 7 - 4
\]
\[
d = 3
\]
**Conclusion:**
The price of a trinket is \( \$2 \) and the price of a doodad is \( \$3 \).
Thus, the final answer is:
- Trinkets cost \( \$2 \)
- Doodads cost \( \$3 \)
Quick Answer
Trinkets cost \( \$2 \) and doodads cost \( \$3 \).
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