Two coffees and three pastries cost £9.50. One coffee and two pastries cost £5.50. Find the cost of one coffee and the cost of one pastry. (3)
Question 1 Report
Two coffees and three pastries cost £9.50. One coffee and two pastries cost £5.50.
Find the cost of one coffee and the cost of one pastry. (3)
Answer Details
This problem needs to be translated into two simultaneous equations before it can be solved: let \(c\) be the cost of one coffee and \(p\) the cost of one pastry, in pounds.
- [3] The two purchases give \[2c + 3p = 9.50 \qquad \text{and} \qquad c + 2p = 5.50.\] Multiplying the second equation by 2 makes the coffee terms match: \[2c + 4p = 11.00.\] Subtracting the first equation from this: \[(2c+4p) - (2c+3p) = 11.00 - 9.50 \implies p = 1.50.\] Substituting back into \(c+2p=5.50\): \[c = 5.50 - 2(1.50) = 5.50 - 3.00 = 2.50.\] So one coffee costs \(£2.50\) and one pastry costs \(£1.50\).
Multiplying an equation by a constant so that one variable's coefficient matches in both equations is the standard first step whenever the coefficients are not already equal, as here with the coffee terms \(2c\) and \(c\).
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