Thank you for visiting Alex and Ben go to a cafe with some friends Alex buys 4 cups of coffee and 3 cups of tea He pays a total. 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!
Answer :
Final answer:
To solve for the cost of a cup of coffee and a cup of tea, we set up a system of equations based on the purchases of Alex and Ben. After solving, we find that the cost of each cup of coffee is £1.10 and each cup of tea is £0.85.
Explanation:
To determine the cost of each cup of coffee and each cup of tea, we must solve a system of equations based on the information provided about Alex and Ben's purchases at the cafe. Let's define x to be the cost of a cup of coffee and y to be the cost of a cup of tea.
Alex's purchase gives us the first equation. He buys 4 cups of coffee and 3 cups of tea and pays a total of £6.95. So, the first equation is:
4x + 3y = 6.95
Ben's purchase gives us the second equation. He buys 5 cups of coffee and 2 cups of tea and pays a total of £7.20. So, the second equation is:
5x + 2y = 7.20
We now solve this system of equations using either substitution or elimination. For this example, let's use the elimination method by multiplying the first equation by 2 and the second equation by 3 to eliminate y:
(4x + 3y) × 2 = 6.95 × 2
(5x + 2y) × 3 = 7.20 × 3
This yields:
8x + 6y = 13.90
15x + 6y = 21.60
Subtracting the first new equation from the second new equation, we get:
7x = 7.70
Dividing both sides by 7:
x = 1.10
Now we know the cost of a cup of coffee (£1.10). We can substitute this value back into either of the original equations to find y. Using Alex's equation:
4(1.10) + 3y = 6.95
4.40 + 3y = 6.95
3y = 6.95 - 4.40
3y = 2.55
Dividing both sides by 3:
y = 0.85
So, the cost of a cup of tea is £0.85. In conclusion, each cup of coffee costs £1.10 and each cup of tea costs £0.85.
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Rewritten by : Jeany
c - the cost of one cup of coffee
t - the cost of one cup of tea
1. (4c + 3t=6.95)*2 -----> 8c+6t=13.90 (1)
(5c + 2t =7.20) *(-3) ---->-15c-6t=-21.60 (2)
2. Add equation (1) and (2)
-7c= - 7.70, c=1.10 Cup of Coffee £ 1.10
3. substitute 1.10 into the first equation
4c + 3t=6.95, 4*1.10 + 3t=6.95, 3t = 6.95-4.40 =2.55, t= £ 0.85 cup of tea
t - the cost of one cup of tea
1. (4c + 3t=6.95)*2 -----> 8c+6t=13.90 (1)
(5c + 2t =7.20) *(-3) ---->-15c-6t=-21.60 (2)
2. Add equation (1) and (2)
-7c= - 7.70, c=1.10 Cup of Coffee £ 1.10
3. substitute 1.10 into the first equation
4c + 3t=6.95, 4*1.10 + 3t=6.95, 3t = 6.95-4.40 =2.55, t= £ 0.85 cup of tea
