Two classes fund-raise for school sports day by selling wristbands at \(x\) pounds and badges at \(y\) pounds. Class A sells 4 wristbands and 6 badges for £...
Question 1 Report
Two classes fund-raise for school sports day by selling wristbands at \(x\) pounds and badges at \(y\) pounds. Class A sells 4 wristbands and 6 badges for £38. Class B sells 7 wristbands and 2 badges for £41.
- Write down an equation for Class A's sales. (1)
- Write down an equation for Class B's sales. (1)
- Find the price of one wristband and one badge. (3)
Answer Details
Scaling the second equation to match the coefficient of \(y\) in the first allows \(y\) to be eliminated by subtraction.
(a) Four wristbands and six badges sell for £38: \(4x + 6y = 38\). [1 mark]
(b) Seven wristbands and two badges sell for £41: \(7x + 2y = 41\). [1 mark]
(c) Multiplying the second equation by 3 gives \(21x + 6y = 123\). Subtracting the first equation eliminates \(y\): \(17x = 85\), so \(x = 5\). Substituting into the second equation, \(7(5) + 2y = 41\), so \(2y = 6\), giving \(y = 3\). One wristband costs £5 and one badge costs £3. [3 marks]
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