The cost of a lunch of 3 sandwiches, 7 cups of coffee and 1 donut is $3.15. The cost of a lunch of 4 sandwiches, 10 cups of coffee and 1 donut was $4.20 at the same cafe.
How much will 1 sandwich, 1 cup of coffee and 1 donut cost?
s= sandwich cost
c= coffee
d= donut
3s+7c+d = 3.15
3.15 - 9c +7c + d = 3.15
-2c+d = 0
d = 2c
1s+1c+1d = 1.05 - 3c +1c +2c = 1.05
3s + 7c + 1d = 315
4s + 10c + 1d = 420
subtract them
s + 3c = 105
s = 105-3c
sub back into 1st
3(105-3c) + 7c + d = 315
d = 2c
s+c+d
= 105-3c + c + 2c
=105
cost = $1.05
To find the cost of 1 sandwich, 1 cup of coffee, and 1 donut, we need to solve for the variables using the given information.
We are given two equations:
Equation 1: 3s + 7c + d = 3.15
Equation 2: 4s + 10c + d = 4.20
From Equation 1, we can rearrange it to solve for d in terms of c and substitute into Equation 2:
d = 2c
Substituting d = 2c into Equation 2:
4s + 10c + 2c = 4.20
4s + 12c = 4.20
Now, we have two equations with two variables:
3s + 7c + d = 3.15
4s + 12c = 4.20
To solve this system of equations, we can use either substitution or elimination method. Let's use elimination:
Multiply the first equation by 4:
12s + 28c + 4d = 12.60
Subtract the above equation from the second equation:
(4s + 12c) - (12s + 28c + 4d) = 4.20 - 12.60
Simplifying:
4s + 12c - 12s - 28c - 4d = -8.40
-8s - 16c - 4d = -8.40
Now, we have the following equation:
-8s - 16c - 4d = -8.40 (Equation 3)
Next, we need to solve for s in terms of c:
Equation 1: 3s + 7c + d = 3.15
Rearrange it:
3s = 3.15 - 7c - d
s = (3.15 - 7c - d)/3 (Equation 4)
Substitute Equation 4 into Equation 3:
-8(3.15 - 7c - d)/3 - 16c - 4d = -8.40
Simplify:
-25.2 + 56/3c + 8/3d - 16c - 4d = -8.40
-25.2 - 45c - 12d + 24c + 12d = -8.40
Combine like terms:
-21.2 - 21c = -8.40
Now, solve for c:
-21c = -8.40 + 21.2
-21c = 12.8
c = 12.8 / -21
c ≈ -0.609
We have found the value of c, which is approximately -0.609. However, the cost cannot be negative. This suggests that there may be an error in the given information or calculations.
Please double-check the given information and calculations to ensure accuracy.