At the school sports day, ticket income is calculated using the formula \(R = 3.5a + 1.5c\), where \(R\) is the total income in pounds, \(a\) is the number ...
Question 1 Report
At the school sports day, ticket income is calculated using the formula \(R = 3.5a + 1.5c\), where \(R\) is the total income in pounds, \(a\) is the number of adult tickets sold and \(c\) is the number of child tickets sold. On Friday, the school sold 42 adult tickets and 65 child tickets.
- Work out the total income on Friday. (2)
- On Saturday, the income was £312.50, from 55 adult tickets and an unknown number of child tickets. Find the number of child tickets sold. (3)
Answer Details
This question tests substituting into a formula with two variables, then using one known total to find the other variable.
- Substituting \(a = 42\), \(c = 65\) into \(R = 3.5a + 1.5c\): \(R = 3.5(42) + 1.5(65) = 147 + 97.5 = £244.50\). [2]
- Substituting \(R = 312.50\), \(a = 55\): \(3.5(55) = 192.5\), so \(1.5c = 312.5 - 192.5 = 120\), giving \(c = 120 \div 1.5 = 80\) child tickets. [3]
Part (b) is testing that the known variable, \(a\), is substituted and its contribution subtracted from the total income first, leaving a simple one-step equation in \(c\) to solve, rather than trying to rearrange the two-variable formula directly.
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