Let \( p \) be the number of apples needed for one apple pie, and \( t \) be the number of apples needed for one apple tart. We can establish a system of equations based on the information provided about Jada and Laura's baking.
For Jada:
- She baked 8 apple pies and 1 apple tart, which used a total of 70 apples. This gives us the equation: \[ 8p + 1t = 70 \quad \text{(1)} \]
For Laura:
- She made 3 apple pies and 5 apple tarts, which used a total of 54 apples. This gives us the equation: \[ 3p + 5t = 54 \quad \text{(2)} \]
Now we have the system of equations:
- \( 8p + t = 70 \)
- \( 3p + 5t = 54 \)
Solving the System of Equations
From equation (1), we can express \( t \) in terms of \( p \): \[ t = 70 - 8p \quad \text{(3)} \]
Now, we can substitute equation (3) into equation (2): \[ 3p + 5(70 - 8p) = 54 \] Expanding this: \[ 3p + 350 - 40p = 54 \] Combining like terms: \[ -37p + 350 = 54 \] Subtracting 350 from both sides: \[ -37p = 54 - 350 \] \[ -37p = -296 \] Dividing by -37: \[ p = \frac{296}{37} = 8 \]
Now that we have \( p \), we can substitute back to find \( t \): Using equation (3): \[ t = 70 - 8(8) \] \[ t = 70 - 64 \] \[ t = 6 \]
Final Answer
An apple pie uses 8 apples and an apple tart requires 6 apples.
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