Jack and Jill went to burger queen. Jack bought 2 hamburgers and 3 milkshakes for $4.21 while Jill bought 3 hamburgers and 2 milkshakes for $5.24. The cost of 1 hamburger and 1 shake is
a. $1.03
b. $1.54
c. $1.89
d. $9.45
2 h + 3 m = 4.21 ... 6 h + 9 m = 12.63
3 h + 2 m = 5.24 ... 6 h + 4 m = 10.48
solve the system for h and m
... subtract the two equations to eliminate h
2x+3y = 4.21
3x+2y = 5.24
Multiply Eq1 by 3 and Eq2 by 2 and subtract Eq1 from Eq2:
6x+9y = 12.63
6x+4y = 10.48
Diff: 5y = 2.15
Y = $0.43/milkshake.
In Eq1, replace Y with 0.43 and solve for X:
2x+3*0.43 = 4.21
To find the cost of 1 hamburger and 1 shake, we can set up a system of equations based on the given information:
Let's denote the cost of 1 hamburger as 'h' and the cost of 1 milkshake as 'm'.
From the information given, we can write the following equations:
2h + 3m = 4.21 (equation 1) (for Jack's order)
3h + 2m = 5.24 (equation 2) (for Jill's order)
To solve this system of equations, we can use the method of substitution.
Step 1: Solve equation 1 for h in terms of m:
2h = 4.21 - 3m
h = (4.21 - 3m)/2 (equation 3)
Step 2: Substitute equation 3 into equation 2:
3[(4.21 - 3m)/2] + 2m = 5.24
Step 3: Simplify and solve for m:
(12.63 - 9m)/2 + 2m = 5.24
12.63 - 9m + 4m = 10.48
-5m = -2.15
m = 0.43
Step 4: Substitute the value of m back into equation 3 to find h:
h = (4.21 - 3 * 0.43)/2
h = (4.21 - 1.29)/2
h = 0.96
Therefore, the cost of 1 hamburger and 1 shake is $0.96 + $0.43 = $1.39.
The closest answer choice is not provided, so none of the options: (a) $1.03, (b) $1.54, (c) $1.89, or (d) $9.45 is correct.
To find the cost of 1 hamburger (H) and 1 milkshake (M), we need to set up a system of equations based on the given information.
Let's denote the cost of 1 hamburger as 'x' and the cost of 1 milkshake as 'y'.
From the first piece of information, Jack bought 2 hamburgers and 3 milkshakes for $4.21. We can write this as the equation:
2x + 3y = 4.21
From the second piece of information, Jill bought 3 hamburgers and 2 milkshakes for $5.24. We can write this as the equation:
3x + 2y = 5.24
Now, we have a system of two equations with two variables:
2x + 3y = 4.21 (Equation 1)
3x + 2y = 5.24 (Equation 2)
We can solve this system of equations using one of the following methods: substitution, elimination, or matrices. Let's use the elimination method:
Multiply Equation 1 by 2 and Equation 2 by 3 to eliminate the 'x' variable:
4x + 6y = 8.42 (Equation 3)
9x + 6y = 15.72 (Equation 4)
Now, subtract Equation 4 from Equation 3 to eliminate the 'y' variable:
(4x + 6y) - (9x + 6y) = 8.42 - 15.72
-5x = -7.30
x = 1.46
Substitute the value of 'x' back into Equation 1 or Equation 2 to find the value of 'y':
2(1.46) + 3y = 4.21
2.92 + 3y = 4.21
3y = 4.21 - 2.92
3y = 1.29
y = 0.43
So, the cost of 1 hamburger (x) is $1.46 and the cost of 1 milkshake (y) is $0.43.
Now, to calculate the cost of 1 hamburger and 1 milkshake, we simply add the costs together:
Cost of 1 hamburger + Cost of 1 milkshake = $1.46 + $0.43 = $1.89
Therefore, the answer is c. $1.89.