A tuition centre charges its fee per session using the formula $F = \dfrac{5a - 7}{a + 1} + 2b$ dollars, where $a$ is the student's level number and $b$ is the number of subjects taken. Find $F$ when $a = 3$ and $b = 4$.
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Worked Solution
Step 1: Substitute $a = 3$ and $b = 4$ into each part of the expression separately, respecting brackets and the fraction bar.\n
Step 2: Compute the NUMERATOR: $5a - 7 = 5(3) - 7 = 15 - 7 = 8$.\n
Step 3: Compute the DENOMINATOR: $a + 1 = 3 + 1 = 4$.\n
Step 4: Compute the first term (the fraction): $\dfrac{8}{4} = 2$.\n
Step 5: Compute the second term: $2b = 2(4) = 8$.\n
Step 6: Combine: $F = 2 + 8 = 10$. So $F = \$10$.\nCheck: substitute back — $\dfrac{5(3) - 7}{3 + 1} + 2(4) = \dfrac{8}{4} + 8 = 2 + 8 = 10$. ✓
Answer: $10
Correct answer: $10
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