High School

Thank you for visiting At a café 1 Two teas and one coffee cost 3 40 2 One tea and four coffees cost 7 30 Work out the cost. 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:

1. Two teas and one coffee cost £3.40.
2. One tea and four coffees cost £7.30.

Work out the cost of one tea and the cost of one coffee. Provide a step-by-step explanation.

Answer :

The cost of 1 tea is approximately £0.90 and the cost of 1 coffee is approximately £1.60.

To solve this problem, let's assign variables to the unknown quantities:

Let's say the cost of 1 tea is "t" (in pounds) and the cost of 1 coffee is "c" (in pounds).

From the given information, we have the following equations:

Equation 1: 2t + c = 3.40

Equation 2: t + 4c = 7.30

Step 2: Solve the equations

We can use a method called substitution to solve this system of equations. Let's solve Equation 1 for "c":

From Equation 1: c = 3.40 - 2t

Substitute this value of "c" into Equation 2:

t + 4(3.40 - 2t) = 7.30

t + 13.60 - 8t = 7.30

-7t + 13.60 = 7.30

-7t = 7.30 - 13.60

-7t = -6.30

Divide both sides by -7 to isolate "t":

t = (-6.30) / (-7)

t ≈ 0.90

Step 3: Find the cost of 1 coffee

Substitute the value of "t" into Equation 1 to find the cost of 1 coffee:

2(0.90) + c = 3.40

1.80 + c = 3.40

c = 3.40 - 1.80

c ≈ 1.60

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