1 curry and 1 tea cost £4.
2 curries and 2 puddings cost £9.
1 pudding and 2 teas cost £2.
What do you have to pay in total for
1 curry, 1 pudding and 1 tea?
What does each item cost on its own?
c+t = 4
2c+2p = 9
p+2t = 2
c = 3.5
t = 0.5
p = 1
c+t+p = 5
To find out the total cost of 1 curry, 1 pudding, and 1 tea, we can use the given information.
Let's assign variables to the cost of each item:
Let C represent the cost of 1 curry.
Let P represent the cost of 1 pudding.
Let T represent the cost of 1 tea.
From the first statement, we know that 1 curry and 1 tea cost £4. So, we have the equation:
C + T = 4 ----(1)
From the second statement, we know that 2 curries and 2 puddings cost £9. So, we have the equation:
2C + 2P = 9 ----(2)
From the third statement, we know that 1 pudding and 2 teas cost £2. So, we have the equation:
P + 2T = 2 ----(3)
We can now solve these three equations to find the individual costs and the total cost.
To start, let's solve equations (1) and (3) simultaneously:
From equation (1), we have C + T = 4, which can be rewritten as C = 4 - T.
Substituting C = 4 - T into equation (3), we get:
(4 - T) + 2T = 2
Simplifying, we have:
4 - T + 2T = 2
4 + T = 2
T = 2 - 4
T = -2
We have found that the cost of 1 tea is -£2. However, this doesn't make sense as prices should be positive. Let's try solving equations (1) and (2) instead.
From equation (1), we have C + T = 4, which can be rewritten as C = 4 - T.
Substituting C = 4 - T into equation (2), we get:
2(4 - T) + 2P = 9
8 - 2T + 2P = 9
-2T + 2P = 1 ----(4)
Now we can solve equations (3) and (4) simultaneously:
From equation (3), we have P + 2T = 2, which can be rewritten as P = 2 - 2T.
Substituting P = 2 - 2T into equation (4), we get:
-2T + 2(2 - 2T) = 1
-2T + 4 - 4T = 1
-6T + 4 = 1
-6T = 1 - 4
-6T = -3
T = (-3)/(-6)
T = 0.5
We have found that the cost of 1 tea is £0.5.
Now, let's substitute T = 0.5 back into equation (1) to find the cost of 1 curry:
C + 0.5 = 4
C = 4 - 0.5
C = 3.5
We have found that the cost of 1 curry is £3.5.
Finally, let's substitute C = 3.5 and T = 0.5 into equation (2) to find the cost of 1 pudding:
2(3.5) + 2P = 9
7 + 2P = 9
2P = 9 - 7
2P = 2
P = 2/2
P = 1
We have found that the cost of 1 pudding is £1.
To find the total cost of 1 curry, 1 pudding, and 1 tea, we can simply add the individual costs:
Total cost = C + P + T
Total cost = £3.5 + £1 + £0.5
Total cost = £5
Therefore, the total cost for 1 curry, 1 pudding, and 1 tea is £5.
Summary of costs for each item:
- 1 curry costs £3.5
- 1 pudding costs £1
- 1 tea costs £0.5
To find the cost of each item individually, we need to solve the given system of equations.
Let's assign variables to each item:
Let C = cost of 1 curry
Let T = cost of 1 tea
Let P = cost of 1 pudding
From the given information, we can write the following equations:
Equation 1: C + T = £4
Equation 2: 2C + 2P = £9
Equation 3: P + 2T = £2
To solve this system of equations, we can use substitution or elimination method. Let's use substitution method.
From Equation 1, we can solve for C:
C = £4 - T
Now substitute the value of C in Equation 2:
2(£4 - T) + 2P = £9
8 - 2T + 2P = £9
2P - 2T = £1 --- Equation 4
Similarly, we can solve for P in terms of T from Equation 3:
P = £2 - 2T
Now substitute the value of P in Equation 4:
2(£2 - 2T) - 2T = £1
4 - 4T - 2T = £1
-6T = -3
T = £0.50
Substitute the value of T in Equation 1:
C + £0.50 = £4
C = £3.50
Substitute the value of T in Equation 3:
P + 2(£0.50) = £2
P + £1 = £2
P = £1
Therefore, the cost of each item individually is:
1 curry (C) = £3.50
1 tea (T) = £0.50
1 pudding (P) = £1
To find the total cost for 1 curry, 1 pudding, and 1 tea, we add the individual costs:
Total cost = C + P + T
Total cost = £3.50 + £1 + £0.50
Total cost = £5
Therefore, you have to pay £5 in total for 1 curry, 1 pudding, and 1 tea.