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2 CDs and 9 DVDs cost £69. 2 CDs and 6 DVDs cost £48. i. Form a pair of simultaneous equations to represent these two sentences ii. Solve the simultaneous equations to find the cost of 1 CD and 1 DVD.

User Agurchand
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1 Answer

3 votes

Answer:

Cost of 1 CD = x = £3

Cost of 1 DVD = y = £7

Explanation:

Let us represent:

Cost of 1 CD = x

Cost of 1 DVD = y

i. Form a pair of simultaneous equations to represent these two sentences

2 CDs and 9 DVDs cost £69.

2x + 9y = 69.... Equation 1

2 CDs and 6 DVDs cost £48.

2x + 6y = 48..... Equation 2

ii. Solve the simultaneous equations to find the cost of 1 CD and 1 DVD.

Combining both equations together:

2x + 9y = 69.... Equation 1

2x + 6y = 48..... Equation 2

We substract Equation 2 from Equation 1

3y = 21

y = £7

Solving for x using Equation 1

2x + 9y = 69.... Equation 1

2x + 9 × 7 = 69

2x + 63 = 69

Collect like terms

2x = 69 - 63

2x = 6

x = 6/2

x = £3

Therefore,

Cost of 1 CD = x = £3

Cost of 1 DVD = y = £7

User Tsuharesu
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