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 \( \$ 2 \).

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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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