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Thank you for visiting At a café 3 teas and 1 coffee cost 5 10 1 tea and 4 coffees cost 8 30 Work out the cost of 1. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

At a café,

- 3 teas and 1 coffee cost £5.10
- 1 tea and 4 coffees cost £8.30

Work out the cost of 1 tea and the cost of 1 coffee.

Answer :

Final answer:

The cost of 1 tea is £1.10 and the cost of 1 coffee is £1.80, found by solving a system of linear equations representing their combined costs.

Explanation:

To determine the cost of 1 tea and the cost of 1 coffee, we will set up a system of linear equations using the information provided from the café's pricing. Let's denote the cost of 1 tea as T and the cost of 1 coffee as C. We have two equations based on the given information:

3T + C = 5.10 (3 teas and 1 coffee cost £5.10)

T + 4C = 8.30 (1 tea and 4 coffees cost £8.30)

Let's solve the system using substitution or elimination. First, we can multiply the first equation by 4:

12T + 4C = 20.40 (Multiplying the first equation by 4)

Now we will subtract the second equation from the modified first equation to eliminate C:

12T + 4C - (T + 4C) = 20.40 - 8.30

11T = 12.10

Dividing both sides by 11 gives us:

T = 1.10

With the cost of 1 tea known, we can substitute T = 1.10 back into either of the original equations to find C. Let's use the first equation:

3(1.10) + C = 5.10

3.30 + C = 5.10

Subtracting 3.30 from both sides, we find:

C = 1.80

Therefore, the cost of 1 tea is £1.10 and the cost of 1 coffee is £1.80.

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Rewritten by : Jeany

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