Answer:
Explanation:
Let's solve this problem step by step.
First, let's assign variables to the unknown costs. Let's say the cost of a salad is S, the cost of a sandwich is D, and the cost of a drink is X.
Now, let's set up two equations based on the given information:
Equation 1: 3S + 2D + X = 17.75 (Three salads, two sandwiches, and one drink cost $17.75)
Equation 2: S + D + 3X = 10.75 (One salad, one sandwich, and three drinks cost $10.75)
Since we know that a salad costs twice as much as a drink, we can write an additional equation:
Equation 3: S = 2X
Now, let's solve the system of equations using substitution:
Substitute Equation 3 into Equation 1:
3(2X) + 2D + X = 17.75
6X + 2D + X = 17.75
7X + 2D = 17.75 ----(Equation 4)
Substitute Equation 3 into Equation 2:
2X + D + 3X = 10.75
5X + D = 10.75 ----(Equation 5)
Now, we have a system of two equations (Equation 4 and Equation 5) with two variables (X and D). We can solve this system by substitution or elimination.
Let's use elimination. Multiply Equation 5 by 2 to make the coefficients of D the same:
10X + 2D = 21.5 ----(Equation 6)
Now, subtract Equation 6 from Equation 4 to eliminate D:
(7X + 2D) - (10X + 2D) = 17.75 - 21.5
7X - 10X = -3.75
-3X = -3.75
X = 1.25
Now, substitute X = 1.25 into Equation 5 to find D:
5(1.25) + D = 10.75
6.25 + D = 10.75
D = 10.75 - 6.25
D = 4.50
Finally, substitute X = 1.25 and D = 4.50 into Equation 3 to find S:
S = 2(1.25)
S = 2.50
Therefore, a salad costs $2.50, a sandwich costs $4.50, and a drink costs $1.25.